iGraph Demo

Based on: Network Analysis and Visualization with R and igraph Katherine Ognyanova, www.kateto.net NetSciX 2016 School of Code Workshop, Wroclaw, Poland http://kateto.net/networks-r-igraph

v1 <- 2
v2 <- 3
(v1 >2) | (v2>0)

[1] TRUE

(v1 >2) || (v2>0)

[1] TRUE

par(bg="gray40")
col.tr <- grDevices::adjustcolor("557799", alpha=0.7)
plot(x=1:5, y=rep(5,5), pch=19, cex=12, col=col.tr, xlim=c(0,6)) 

colors()                          # List all named colors

  [1] "white"                "aliceblue"            "antiquewhite"        
  [4] "antiquewhite1"        "antiquewhite2"        "antiquewhite3"       
  [7] "antiquewhite4"        "aquamarine"           "aquamarine1"         
 [10] "aquamarine2"          "aquamarine3"          "aquamarine4"         
 [13] "azure"                "azure1"               "azure2"              
 [16] "azure3"               "azure4"               "beige"               
 [19] "bisque"               "bisque1"              "bisque2"             
 [22] "bisque3"              "bisque4"              "black"               
 [25] "blanchedalmond"       "blue"                 "blue1"               
 [28] "blue2"                "blue3"                "blue4"               
 [31] "blueviolet"           "brown"                "brown1"              
 [34] "brown2"               "brown3"               "brown4"              
 [37] "burlywood"            "burlywood1"           "burlywood2"          
 [40] "burlywood3"           "burlywood4"           "cadetblue"           
 [43] "cadetblue1"           "cadetblue2"           "cadetblue3"          
 [46] "cadetblue4"           "chartreuse"           "chartreuse1"         
 [49] "chartreuse2"          "chartreuse3"          "chartreuse4"         
 [52] "chocolate"            "chocolate1"           "chocolate2"          
 [55] "chocolate3"           "chocolate4"           "coral"               
 [58] "coral1"               "coral2"               "coral3"              
 [61] "coral4"               "cornflowerblue"       "cornsilk"            
 [64] "cornsilk1"            "cornsilk2"            "cornsilk3"           
 [67] "cornsilk4"            "cyan"                 "cyan1"               
 [70] "cyan2"                "cyan3"                "cyan4"               
 [73] "darkblue"             "darkcyan"             "darkgoldenrod"       
 [76] "darkgoldenrod1"       "darkgoldenrod2"       "darkgoldenrod3"      
 [79] "darkgoldenrod4"       "darkgray"             "darkgreen"           
 [82] "darkgrey"             "darkkhaki"            "darkmagenta"         
 [85] "darkolivegreen"       "darkolivegreen1"      "darkolivegreen2"     
 [88] "darkolivegreen3"      "darkolivegreen4"      "darkorange"          
 [91] "darkorange1"          "darkorange2"          "darkorange3"         
 [94] "darkorange4"          "darkorchid"           "darkorchid1"         
 [97] "darkorchid2"          "darkorchid3"          "darkorchid4"         
[100] "darkred"              "darksalmon"           "darkseagreen"        
[103] "darkseagreen1"        "darkseagreen2"        "darkseagreen3"       
[106] "darkseagreen4"        "darkslateblue"        "darkslategray"       
[109] "darkslategray1"       "darkslategray2"       "darkslategray3"      
[112] "darkslategray4"       "darkslategrey"        "darkturquoise"       
[115] "darkviolet"           "deeppink"             "deeppink1"           
[118] "deeppink2"            "deeppink3"            "deeppink4"           
[121] "deepskyblue"          "deepskyblue1"         "deepskyblue2"        
[124] "deepskyblue3"         "deepskyblue4"         "dimgray"             
[127] "dimgrey"              "dodgerblue"           "dodgerblue1"         
[130] "dodgerblue2"          "dodgerblue3"          "dodgerblue4"         
[133] "firebrick"            "firebrick1"           "firebrick2"          
[136] "firebrick3"           "firebrick4"           "floralwhite"         
[139] "forestgreen"          "gainsboro"            "ghostwhite"          
[142] "gold"                 "gold1"                "gold2"               
[145] "gold3"                "gold4"                "goldenrod"           
[148] "goldenrod1"           "goldenrod2"           "goldenrod3"          
[151] "goldenrod4"           "gray"                 "gray0"               
[154] "gray1"                "gray2"                "gray3"               
[157] "gray4"                "gray5"                "gray6"               
[160] "gray7"                "gray8"                "gray9"               
[163] "gray10"               "gray11"               "gray12"              
[166] "gray13"               "gray14"               "gray15"              
[169] "gray16"               "gray17"               "gray18"              
[172] "gray19"               "gray20"               "gray21"              
[175] "gray22"               "gray23"               "gray24"              
[178] "gray25"               "gray26"               "gray27"              
[181] "gray28"               "gray29"               "gray30"              
[184] "gray31"               "gray32"               "gray33"              
[187] "gray34"               "gray35"               "gray36"              
[190] "gray37"               "gray38"               "gray39"              
[193] "gray40"               "gray41"               "gray42"              
[196] "gray43"               "gray44"               "gray45"              
[199] "gray46"               "gray47"               "gray48"              
[202] "gray49"               "gray50"               "gray51"              
[205] "gray52"               "gray53"               "gray54"              
[208] "gray55"               "gray56"               "gray57"              
[211] "gray58"               "gray59"               "gray60"              
[214] "gray61"               "gray62"               "gray63"              
[217] "gray64"               "gray65"               "gray66"              
[220] "gray67"               "gray68"               "gray69"              
[223] "gray70"               "gray71"               "gray72"              
[226] "gray73"               "gray74"               "gray75"              
[229] "gray76"               "gray77"               "gray78"              
[232] "gray79"               "gray80"               "gray81"              
[235] "gray82"               "gray83"               "gray84"              
[238] "gray85"               "gray86"               "gray87"              
[241] "gray88"               "gray89"               "gray90"              
[244] "gray91"               "gray92"               "gray93"              
[247] "gray94"               "gray95"               "gray96"              
[250] "gray97"               "gray98"               "gray99"              
[253] "gray100"              "green"                "green1"              
[256] "green2"               "green3"               "green4"              
[259] "greenyellow"          "grey"                 "grey0"               
[262] "grey1"                "grey2"                "grey3"               
[265] "grey4"                "grey5"                "grey6"               
[268] "grey7"                "grey8"                "grey9"               
[271] "grey10"               "grey11"               "grey12"              
[274] "grey13"               "grey14"               "grey15"              
[277] "grey16"               "grey17"               "grey18"              
[280] "grey19"               "grey20"               "grey21"              
[283] "grey22"               "grey23"               "grey24"              
[286] "grey25"               "grey26"               "grey27"              
[289] "grey28"               "grey29"               "grey30"              
[292] "grey31"               "grey32"               "grey33"              
[295] "grey34"               "grey35"               "grey36"              
[298] "grey37"               "grey38"               "grey39"              
[301] "grey40"               "grey41"               "grey42"              
[304] "grey43"               "grey44"               "grey45"              
[307] "grey46"               "grey47"               "grey48"              
[310] "grey49"               "grey50"               "grey51"              
[313] "grey52"               "grey53"               "grey54"              
[316] "grey55"               "grey56"               "grey57"              
[319] "grey58"               "grey59"               "grey60"              
[322] "grey61"               "grey62"               "grey63"              
[325] "grey64"               "grey65"               "grey66"              
[328] "grey67"               "grey68"               "grey69"              
[331] "grey70"               "grey71"               "grey72"              
[334] "grey73"               "grey74"               "grey75"              
[337] "grey76"               "grey77"               "grey78"              
[340] "grey79"               "grey80"               "grey81"              
[343] "grey82"               "grey83"               "grey84"              
[346] "grey85"               "grey86"               "grey87"              
[349] "grey88"               "grey89"               "grey90"              
[352] "grey91"               "grey92"               "grey93"              
[355] "grey94"               "grey95"               "grey96"              
[358] "grey97"               "grey98"               "grey99"              
[361] "grey100"              "honeydew"             "honeydew1"           
[364] "honeydew2"            "honeydew3"            "honeydew4"           
[367] "hotpink"              "hotpink1"             "hotpink2"            
[370] "hotpink3"             "hotpink4"             "indianred"           
[373] "indianred1"           "indianred2"           "indianred3"          
[376] "indianred4"           "ivory"                "ivory1"              
[379] "ivory2"               "ivory3"               "ivory4"              
[382] "khaki"                "khaki1"               "khaki2"              
[385] "khaki3"               "khaki4"               "lavender"            
[388] "lavenderblush"        "lavenderblush1"       "lavenderblush2"      
[391] "lavenderblush3"       "lavenderblush4"       "lawngreen"           
[394] "lemonchiffon"         "lemonchiffon1"        "lemonchiffon2"       
[397] "lemonchiffon3"        "lemonchiffon4"        "lightblue"           
[400] "lightblue1"           "lightblue2"           "lightblue3"          
[403] "lightblue4"           "lightcoral"           "lightcyan"           
[406] "lightcyan1"           "lightcyan2"           "lightcyan3"          
[409] "lightcyan4"           "lightgoldenrod"       "lightgoldenrod1"     
[412] "lightgoldenrod2"      "lightgoldenrod3"      "lightgoldenrod4"     
[415] "lightgoldenrodyellow" "lightgray"            "lightgreen"          
[418] "lightgrey"            "lightpink"            "lightpink1"          
[421] "lightpink2"           "lightpink3"           "lightpink4"          
[424] "lightsalmon"          "lightsalmon1"         "lightsalmon2"        
[427] "lightsalmon3"         "lightsalmon4"         "lightseagreen"       
[430] "lightskyblue"         "lightskyblue1"        "lightskyblue2"       
[433] "lightskyblue3"        "lightskyblue4"        "lightslateblue"      
[436] "lightslategray"       "lightslategrey"       "lightsteelblue"      
[439] "lightsteelblue1"      "lightsteelblue2"      "lightsteelblue3"     
[442] "lightsteelblue4"      "lightyellow"          "lightyellow1"        
[445] "lightyellow2"         "lightyellow3"         "lightyellow4"        
[448] "limegreen"            "linen"                "magenta"             
[451] "magenta1"             "magenta2"             "magenta3"            
[454] "magenta4"             "maroon"               "maroon1"             
[457] "maroon2"              "maroon3"              "maroon4"             
[460] "mediumaquamarine"     "mediumblue"           "mediumorchid"        
[463] "mediumorchid1"        "mediumorchid2"        "mediumorchid3"       
[466] "mediumorchid4"        "mediumpurple"         "mediumpurple1"       
[469] "mediumpurple2"        "mediumpurple3"        "mediumpurple4"       
[472] "mediumseagreen"       "mediumslateblue"      "mediumspringgreen"   
[475] "mediumturquoise"      "mediumvioletred"      "midnightblue"        
[478] "mintcream"            "mistyrose"            "mistyrose1"          
[481] "mistyrose2"           "mistyrose3"           "mistyrose4"          
[484] "moccasin"             "navajowhite"          "navajowhite1"        
[487] "navajowhite2"         "navajowhite3"         "navajowhite4"        
[490] "navy"                 "navyblue"             "oldlace"             
[493] "olivedrab"            "olivedrab1"           "olivedrab2"          
[496] "olivedrab3"           "olivedrab4"           "orange"              
[499] "orange1"              "orange2"              "orange3"             
[502] "orange4"              "orangered"            "orangered1"          
[505] "orangered2"           "orangered3"           "orangered4"          
[508] "orchid"               "orchid1"              "orchid2"             
[511] "orchid3"              "orchid4"              "palegoldenrod"       
[514] "palegreen"            "palegreen1"           "palegreen2"          
[517] "palegreen3"           "palegreen4"           "paleturquoise"       
[520] "paleturquoise1"       "paleturquoise2"       "paleturquoise3"      
[523] "paleturquoise4"       "palevioletred"        "palevioletred1"      
[526] "palevioletred2"       "palevioletred3"       "palevioletred4"      
[529] "papayawhip"           "peachpuff"            "peachpuff1"          
[532] "peachpuff2"           "peachpuff3"           "peachpuff4"          
[535] "peru"                 "pink"                 "pink1"               
[538] "pink2"                "pink3"                "pink4"               
[541] "plum"                 "plum1"                "plum2"               
[544] "plum3"                "plum4"                "powderblue"          
[547] "purple"               "purple1"              "purple2"             
[550] "purple3"              "purple4"              "red"                 
[553] "red1"                 "red2"                 "red3"                
[556] "red4"                 "rosybrown"            "rosybrown1"          
[559] "rosybrown2"           "rosybrown3"           "rosybrown4"          
[562] "royalblue"            "royalblue1"           "royalblue2"          
[565] "royalblue3"           "royalblue4"           "saddlebrown"         
[568] "salmon"               "salmon1"              "salmon2"             
[571] "salmon3"              "salmon4"              "sandybrown"          
[574] "seagreen"             "seagreen1"            "seagreen2"           
[577] "seagreen3"            "seagreen4"            "seashell"            
[580] "seashell1"            "seashell2"            "seashell3"           
[583] "seashell4"            "sienna"               "sienna1"             
[586] "sienna2"              "sienna3"              "sienna4"             
[589] "skyblue"              "skyblue1"             "skyblue2"            
[592] "skyblue3"             "skyblue4"             "slateblue"           
[595] "slateblue1"           "slateblue2"           "slateblue3"          
[598] "slateblue4"           "slategray"            "slategray1"          
[601] "slategray2"           "slategray3"           "slategray4"          
[604] "slategrey"            "snow"                 "snow1"               
[607] "snow2"                "snow3"                "snow4"               
[610] "springgreen"          "springgreen1"         "springgreen2"        
[613] "springgreen3"         "springgreen4"         "steelblue"           
[616] "steelblue1"           "steelblue2"           "steelblue3"          
[619] "steelblue4"           "tan"                  "tan1"                
[622] "tan2"                 "tan3"                 "tan4"                
[625] "thistle"              "thistle1"             "thistle2"            
[628] "thistle3"             "thistle4"             "tomato"              
[631] "tomato1"              "tomato2"              "tomato3"             
[634] "tomato4"              "turquoise"            "turquoise1"          
[637] "turquoise2"           "turquoise3"           "turquoise4"          
[640] "violet"               "violetred"            "violetred1"          
[643] "violetred2"           "violetred3"           "violetred4"          
[646] "wheat"                "wheat1"               "wheat2"              
[649] "wheat3"               "wheat4"               "whitesmoke"          
[652] "yellow"               "yellow1"              "yellow2"             
[655] "yellow3"              "yellow4"              "yellowgreen"         

grep("blue", colors(), value=T)   # Colors that have "blue" in the name

 [1] "aliceblue"       "blue"            "blue1"           "blue2"          
 [5] "blue3"           "blue4"           "blueviolet"      "cadetblue"      
 [9] "cadetblue1"      "cadetblue2"      "cadetblue3"      "cadetblue4"     
[13] "cornflowerblue"  "darkblue"        "darkslateblue"   "deepskyblue"    
[17] "deepskyblue1"    "deepskyblue2"    "deepskyblue3"    "deepskyblue4"   
[21] "dodgerblue"      "dodgerblue1"     "dodgerblue2"     "dodgerblue3"    
[25] "dodgerblue4"     "lightblue"       "lightblue1"      "lightblue2"     
[29] "lightblue3"      "lightblue4"      "lightskyblue"    "lightskyblue1"  
[33] "lightskyblue2"   "lightskyblue3"   "lightskyblue4"   "lightslateblue" 
[37] "lightsteelblue"  "lightsteelblue1" "lightsteelblue2" "lightsteelblue3"
[41] "lightsteelblue4" "mediumblue"      "mediumslateblue" "midnightblue"   
[45] "navyblue"        "powderblue"      "royalblue"       "royalblue1"     
[49] "royalblue2"      "royalblue3"      "royalblue4"      "skyblue"        
[53] "skyblue1"        "skyblue2"        "skyblue3"        "skyblue4"       
[57] "slateblue"       "slateblue1"      "slateblue2"      "slateblue3"     
[61] "slateblue4"      "steelblue"       "steelblue1"      "steelblue2"     
[65] "steelblue3"      "steelblue4"     

rm(list = ls()) # Remove all the objects we created so far.
library(igraph) # Load the igraph package

package <U+393C><U+3E31>igraph<U+393C><U+3E32> was built under R version 3.3.3
Attaching package: <U+393C><U+3E31>igraph<U+393C><U+3E32>

The following objects are masked from <U+393C><U+3E31>package:stats<U+393C><U+3E32>:

    decompose, spectrum

The following object is masked from <U+393C><U+3E31>package:base<U+393C><U+3E32>:

    union

g1 <- graph( edges=c(1,2, 2,3, 3, 1), n=3, directed=F ) 
g2 <- graph("cubical") 
plot(g1) # A simple plot of the network - we'll talk more about plots later

plot(g2)

class(g1)

[1] "igraph"

g1

IGRAPH b0ac7a8 U--- 3 3 -- 
+ edges from b0ac7a8:
[1] 1--2 2--3 1--3

g3 <- graph( c("John", "Jim", "Jim", "Jill", "Jill", "John")) # named vertices
# When the edge list has vertex names, the number of nodes is not needed
plot(g3)

g4 <- graph( c("John", "Jim", "Jim", "Jack", "Jim", "Jack", "John", "John"), 
             isolates=c("Jesse", "Janis", "Jennifer", "Justin") )  
# In named graphs we can specify isolates by providing a list of their names.
plot(g4, edge.arrow.size=.5, vertex.color="gold", vertex.size=15, 
     vertex.frame.color="gray", vertex.label.color="black", 
     vertex.label.cex=1.8, vertex.label.dist=2.5, edge.curved=0.52) 

Small graphs can also be generated with a description of this kind: - for undirected tie, +- or -+ for directed ties pointing left & right, ++ for a symmetric tie, and “:” for sets of vertices.

plot(graph_from_literal(a++b, b++c)) # the number of dashes doesn't matter

plot(graph_from_literal(a--b, b--c)) # the number of dashes doesn't matter

plot(graph_from_literal(a--+b, b+--c))

plot(graph_from_literal(a:b:c---c:d:e))

gl <- graph_from_literal(a-b-c-d-e-f, a-g-h-b, e-h:f:i:z:d, j)
plot(gl)

2.2 Edge, vertex, and network attributes

Access vertices and edges:

E(g4) # The edges of the object

+ 4/4 edges from b107943 (vertex names):
[1] John->Jim  Jim ->Jack Jim ->Jack John->John

V(g4) # The vertices of the object

+ 7/7 vertices, named, from b107943:
[1] John     Jim      Jack     Jesse    Janis    Jennifer Justin  

You can also examine the network matrix directly:

g4[]

7 x 7 sparse Matrix of class "dgCMatrix"
         John Jim Jack Jesse Janis Jennifer Justin
John        1   1    .     .     .        .      .
Jim         .   .    2     .     .        .      .
Jack        .   .    .     .     .        .      .
Jesse       .   .    .     .     .        .      .
Janis       .   .    .     .     .        .      .
Jennifer    .   .    .     .     .        .      .
Justin      .   .    .     .     .        .      .

g4[1,] 

    John      Jim     Jack    Jesse    Janis Jennifer   Justin 
       1        1        0        0        0        0        0 

Add attributes to the network, vertices, or edges:

V(g4)$name # automatically generated when we created the network.

[1] "John"     "Jim"      "Jack"     "Jesse"    "Janis"    "Jennifer" "Justin"  

V(g4)$gender <- c("male", "male", "male", "male", "female", "female", "male")
E(g4)$type <- "email" # Edge attribute, assign "email" to all edges
E(g4)$weight <- 10    # Edge weight, setting all existing edges to 10

Examine attributes:

edge_attr(g4)

$type
[1] "email" "email" "email" "email"

$weight
[1] 10 10 10 10

vertex_attr(g4)

$name
[1] "John"     "Jim"      "Jack"     "Jesse"    "Janis"    "Jennifer" "Justin"  

$gender
[1] "male"   "male"   "male"   "male"   "female" "female" "male"  

graph_attr(g4)

named list()

Another way to set attributes (you can similarly use set_edge_attr(), set_vertex_attr(), etc.):

g4 <- set_graph_attr(g4, "name", "Email Network")
g4 <- set_graph_attr(g4, "something", "A thing")
graph_attr_names(g4)

[1] "name"      "something"

graph_attr(g4, "name")

[1] "Email Network"

graph_attr(g4)

$name
[1] "Email Network"

$something
[1] "A thing"

g4 <- delete_graph_attr(g4, "something")
graph_attr(g4)

$name
[1] "Email Network"

plot(g4, edge.arrow.size=.5, vertex.label.color="black", vertex.label.dist=1.5,
     vertex.color=c( "pink", "skyblue")[1+(V(g4)$gender=="male")] ) 

The graph g4 has two edges going from Jim to Jack, and a loop from John to himself. We can simplify our graph to remove loops & multiple edges between the same nodes. Use edge.attr.comb to indicate how edge attributes are to be combined - possible options include sum, mean, prod (product), min, max, first/last (selects the first/last edge’s attribute). Option “ignore” says the attribute should be disregarded and dropped.

g4s <- simplify( g4, remove.multiple = T, remove.loops = F, 
                 edge.attr.comb=c(weight="sum", type="ignore") )
plot(g4s, vertex.label.dist=1.5)

g4s

IGRAPH b450ff2 DNW- 7 3 -- Email Network
+ attr: name (g/c), name (v/c), gender (v/c), weight (e/n)
+ edges from b450ff2 (vertex names):
[1] John->John John->Jim  Jim ->Jack

The description of an igraph object starts with up to four letters:

D or U, for a directed or undirected graph N for a named graph (where nodes have a name attribute) W for a weighted graph (where edges have a weight attribute) B for a bipartite (two-mode) graph (where nodes have a type attribute) The two numbers that follow (7 5) refer to the number of nodes and edges in the graph. The description also lists node & edge attributes, for example:

(g/c) - graph-level character attribute (v/c) - vertex-level character attribute (e/n) - edge-level numeric attribute 2.3 Specific graphs and graph models

Empty graph

eg <- make_empty_graph(40)
plot(eg, vertex.size=10, vertex.label=NA)

Full Graph

fg <- make_full_graph(40)
plot(fg, vertex.size=10, vertex.label=NA)

Simple star graph

st <- make_star(40)
plot(st, vertex.size=10, vertex.label=NA) 

Tree graph

tr <- make_tree(40, children = 5, mode = "undirected")
plot(tr, vertex.size=10, vertex.label=NA) 

Ring graph

rn <- make_ring(40)
plot(rn, vertex.size=10, vertex.label=NA)

Erdos-Renyi random graph model (‘n’ is number of nodes, ‘m’ is the number of edges).

er <- sample_gnm(n=100, m=70) 
plot(er, vertex.size=5, vertex.label=NA)  

Watts-Strogatz small-world model Creates a lattice (with dim dimensions and size nodes across dimension) and rewires edges randomly with probability p. The neighborhood in which edges are connected is nei. You can allow loops and multiple edges.

sw <- sample_smallworld(dim=2, size=10, nei=1, p=0.1)
plot(sw, vertex.size=6, vertex.label=NA, layout=layout_in_circle)

Barabasi-Albert preferential attachment model for scale-free graphs (n is number of nodes, power is the power of attachment (1 is linear); m is the number of edges added on each time step)

ba <-  sample_pa(n=100, power=1.5, m=1,  directed=F)
 plot(ba, vertex.size=6, vertex.label=NA)

igraph can also give you some notable historical graphs. For instance:

zach <- graph("Zachary") # the Zachary Karate club
 plot(zach, vertex.size=10, vertex.label=NA)

Rewiring a graph each_edge() is a rewiring method that changes the edge endpoints uniformly randomly with a probability prob.

rn.rewired <- rewire(rn, each_edge(prob=0.1))
 plot(rn.rewired, vertex.size=10, vertex.label=NA)

Rewire to connect vertices to other vertices at a certain distance.

rn.neigh = connect.neighborhood(rn, 6)
 plot(rn.neigh, vertex.size=8, vertex.label=NA) 

Combine graphs (disjoint union, assuming separate vertex sets): %du%

plot(rn, vertex.size=10, vertex.label=NA) 

 plot(tr, vertex.size=10, vertex.label=NA) 

 plot(rn %du% tr, vertex.size=10, vertex.label=NA) 

3. Reading network data from files In the following sections of the tutorial, we will work primarily with two small example data sets. Both contain data about media organizations. One involves a network of hyperlinks and mentions among news sources. The second is a network of links between media venues and consumers. While the example data used here is small, many of the ideas behind the analyses and visualizations we will generate apply to medium and large-scale networks.

3.1 DATASET 1: edgelist

The first data set we are going to work with consists of two files, “Media-Example-NODES.csv” and “Media-Example-EDGES.csv” (download here). http://www.kateto.net/wordpress/wp-content/uploads/2016/01/netscix2016.zip

nodes <- read.csv("G:\\RStudio\\Data\\Dataset1-Media-Example-NODES.csv", header=T, as.is=T)
links <- read.csv("G:\\RStudio\\Data\\Dataset1-Media-Example-EDGES.csv", header=T, as.is=T)

Examine the data:

head(nodes)

head(links)

nrow(nodes) 

[1] 17

length(unique(nodes$id))

[1] 17

nrow(links)

[1] 52

nrow(unique(links[,c("from", "to")]))

[1] 49

Notice that there are more links than unique from-to combinations. That means we have cases in the data where there are multiple links between the same two nodes. We will collapse all links of the same type between the same two nodes by summing their weights, using aggregate() by “from”, “to”, & “type”. We don’t use simplify() here so as not to collapse different link types.

links <- aggregate(links[,3], links[,-3], sum)
links <- links[order(links$from, links$to),]
colnames(links)[4] <- "weight"
rownames(links) <- NULL

3.2 DATASET 2: matrix

Two-mode or bipartite graphs have two different types of actors and links that go across, but not within each type. Our second media example is a network of that kind, examining links between news sources and their consumers.

nodes2 <- read.csv("G:\\RStudio\\Data\\Dataset2-Media-User-Example-NODES.csv", header=T, as.is=T)
links2 <- read.csv("G:\\RStudio\\Data\\Dataset2-Media-User-Example-EDGES.csv", header=T, row.names=1)

Examine the data:

head(nodes2,20)

head(links2,20)

We can see that links2 is an adjacency matrix for a two-mode network:

links2 <- as.matrix(links2)
dim(links2)

[1] 10 20

dim(nodes2)

[1] 30  5

4. Turning networks into igraph objects We start by converting the raw data to an igraph network object. Here we use igraph’s graph.data.frame function, which takes two data frames: d and vertices.

d describes the edges of the network (links). Its first two columns are the IDs of the source and the target node for each edge. The following columns are edge attributes (weight, type, label, or anything else).

Vertices starts with a column of node IDs. Any following columns are interpreted as node attributes.

4.1 Dataset 1

library(igraph)
net <- graph_from_data_frame(d=links, vertices=nodes, directed=T) 
class(net)

[1] "igraph"

net

IGRAPH b800806 DNW- 17 49 -- 
+ attr: name (v/c), media (v/c), media.type (v/n), type.label (v/c),
| audience.size (v/n), type (e/c), weight (e/n)
+ edges from b800806 (vertex names):
 [1] s01->s02 s01->s03 s01->s04 s01->s15 s02->s01 s02->s03 s02->s09 s02->s10 s03->s01
[10] s03->s04 s03->s05 s03->s08 s03->s10 s03->s11 s03->s12 s04->s03 s04->s06 s04->s11
[19] s04->s12 s04->s17 s05->s01 s05->s02 s05->s09 s05->s15 s06->s06 s06->s16 s06->s17
[28] s07->s03 s07->s08 s07->s10 s07->s14 s08->s03 s08->s07 s08->s09 s09->s10 s10->s03
[37] s12->s06 s12->s13 s12->s14 s13->s12 s13->s17 s14->s11 s14->s13 s15->s01 s15->s04
[46] s15->s06 s16->s06 s16->s17 s17->s04

We also have easy access to nodes, edges, and their attributes with:

E(net)       # The edges of the "net" object

+ 49/49 edges from b800806 (vertex names):
 [1] s01->s02 s01->s03 s01->s04 s01->s15 s02->s01 s02->s03 s02->s09 s02->s10 s03->s01
[10] s03->s04 s03->s05 s03->s08 s03->s10 s03->s11 s03->s12 s04->s03 s04->s06 s04->s11
[19] s04->s12 s04->s17 s05->s01 s05->s02 s05->s09 s05->s15 s06->s06 s06->s16 s06->s17
[28] s07->s03 s07->s08 s07->s10 s07->s14 s08->s03 s08->s07 s08->s09 s09->s10 s10->s03
[37] s12->s06 s12->s13 s12->s14 s13->s12 s13->s17 s14->s11 s14->s13 s15->s01 s15->s04
[46] s15->s06 s16->s06 s16->s17 s17->s04

V(net)       # The vertices of the "net" object

+ 17/17 vertices, named, from b800806:
 [1] s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17

E(net)$type  # Edge attribute "type"

 [1] "hyperlink" "hyperlink" "hyperlink" "mention"   "hyperlink" "hyperlink" "hyperlink"
 [8] "hyperlink" "hyperlink" "hyperlink" "hyperlink" "hyperlink" "mention"   "hyperlink"
[15] "hyperlink" "hyperlink" "mention"   "mention"   "hyperlink" "mention"   "mention"  
[22] "hyperlink" "hyperlink" "mention"   "hyperlink" "hyperlink" "mention"   "mention"  
[29] "mention"   "hyperlink" "mention"   "hyperlink" "mention"   "mention"   "mention"  
[36] "hyperlink" "mention"   "hyperlink" "mention"   "hyperlink" "mention"   "mention"  
[43] "mention"   "hyperlink" "hyperlink" "hyperlink" "hyperlink" "mention"   "hyperlink"

V(net)$media # Vertex attribute "media"

 [1] "NY Times"            "Washington Post"     "Wall Street Journal"
 [4] "USA Today"           "LA Times"            "New York Post"      
 [7] "CNN"                 "MSNBC"               "FOX News"           
[10] "ABC"                 "BBC"                 "Yahoo News"         
[13] "Google News"         "Reuters.com"         "NYTimes.com"        
[16] "WashingtonPost.com"  "AOL.com"            

Now that we have our igraph network object, let’s make a first attempt to plot it.

plot(net, edge.arrow.size=.4,vertex.label=NA)

That doesn’t look very good. Let’s start fixing things by removing the loops in the graph.

net <- simplify(net, remove.multiple = F, remove.loops = T) 

You might notice that we could have used simplify to combine multiple edges by summing their weights with a command like simplify(net, edge.attr.comb=list(weight=“sum”,“ignore”)). The problem is that this would also combine multiple edge types (in our data: “hyperlinks” and “mentions”).

If you need them, you can extract an edge list or a matrix from igraph networks.

as_edgelist(net, names=T)

      [,1]  [,2] 
 [1,] "s01" "s02"
 [2,] "s01" "s03"
 [3,] "s01" "s04"
 [4,] "s01" "s15"
 [5,] "s02" "s01"
 [6,] "s02" "s03"
 [7,] "s02" "s09"
 [8,] "s02" "s10"
 [9,] "s03" "s01"
[10,] "s03" "s04"
[11,] "s03" "s05"
[12,] "s03" "s08"
[13,] "s03" "s10"
[14,] "s03" "s11"
[15,] "s03" "s12"
[16,] "s04" "s03"
[17,] "s04" "s06"
[18,] "s04" "s11"
[19,] "s04" "s12"
[20,] "s04" "s17"
[21,] "s05" "s01"
[22,] "s05" "s02"
[23,] "s05" "s09"
[24,] "s05" "s15"
[25,] "s06" "s16"
[26,] "s06" "s17"
[27,] "s07" "s03"
[28,] "s07" "s08"
[29,] "s07" "s10"
[30,] "s07" "s14"
[31,] "s08" "s03"
[32,] "s08" "s07"
[33,] "s08" "s09"
[34,] "s09" "s10"
[35,] "s10" "s03"
[36,] "s12" "s06"
[37,] "s12" "s13"
[38,] "s12" "s14"
[39,] "s13" "s12"
[40,] "s13" "s17"
[41,] "s14" "s11"
[42,] "s14" "s13"
[43,] "s15" "s01"
[44,] "s15" "s04"
[45,] "s15" "s06"
[46,] "s16" "s06"
[47,] "s16" "s17"
[48,] "s17" "s04"

as_adjacency_matrix(net, attr="weight")

17 x 17 sparse Matrix of class "dgCMatrix"

   [[ suppressing 17 column names <U+393C><U+3E31>s01<U+393C><U+3E32>, <U+393C><U+3E31>s02<U+393C><U+3E32>, <U+393C><U+3E31>s03<U+393C><U+3E32> ... ]]

                                                     
s01  . 22 22 21 .  .  .  .  .  .  .  .  .  . 20  .  .
s02 23  . 21  . .  .  .  .  1  5  .  .  .  .  .  .  .
s03 21  .  . 22 1  .  .  4  .  2  1  1  .  .  .  .  .
s04  .  . 23  . .  1  .  .  .  . 22  3  .  .  .  .  2
s05  1 21  .  . .  .  .  .  2  .  .  .  .  . 21  .  .
s06  .  .  .  . .  .  .  .  .  .  .  .  .  .  . 21 21
s07  .  .  1  . .  .  . 22  . 21  .  .  .  4  .  .  .
s08  .  .  2  . .  . 21  . 23  .  .  .  .  .  .  .  .
s09  .  .  .  . .  .  .  .  . 21  .  .  .  .  .  .  .
s10  .  .  2  . .  .  .  .  .  .  .  .  .  .  .  .  .
s11  .  .  .  . .  .  .  .  .  .  .  .  .  .  .  .  .
s12  .  .  .  . .  2  .  .  .  .  .  . 22 22  .  .  .
s13  .  .  .  . .  .  .  .  .  .  . 21  .  .  .  .  1
s14  .  .  .  . .  .  .  .  .  .  1  . 21  .  .  .  .
s15 22  .  .  1 .  4  .  .  .  .  .  .  .  .  .  .  .
s16  .  .  .  . . 23  .  .  .  .  .  .  .  .  .  . 21
s17  .  .  .  4 .  .  .  .  .  .  .  .  .  .  .  .  .

Or data frames describing nodes and edges:

as_data_frame(net, what="edges")

as_data_frame(net, what="vertices")

4.2 Dataset 2

As we have seen above, this time the edges of the network are in a matrix format. We can read those into a graph object using graph_from_incidence_matrix(). In igraph, bipartite networks have a node attribute called type that is FALSE (or 0) for vertices in one mode and TRUE (or 1) for those in the other mode.

head(nodes2)

net2 <- graph_from_incidence_matrix(links2)
table(V(net2)$type)

FALSE  TRUE 
   10    20 

To transform a one-mode network matrix into an igraph object, use instead graph_from_adjacency_matrix().

We can also easily generate bipartite projections for the two-mode network: (co-memberships are easy to calculate by multiplying the network matrix by its transposed matrix, or using igraph’s bipartite.projection() function).

net2.bp <- bipartite.projection(net2)

We can calculate the projections manually as well:

as_incidence_matrix(net2)  %*% t(as_incidence_matrix(net2)) 

    s01 s02 s03 s04 s05 s06 s07 s08 s09 s10
s01   3   0   0   0   0   0   0   0   0   1
s02   0   3   0   0   0   0   0   0   1   0
s03   0   0   4   1   0   0   0   0   1   0
s04   0   0   1   3   1   0   0   0   0   1
s05   0   0   0   1   3   1   0   0   0   1
s06   0   0   0   0   1   3   1   1   0   0
s07   0   0   0   0   0   1   3   1   0   0
s08   0   0   0   0   0   1   1   4   1   0
s09   0   1   1   0   0   0   0   1   3   0
s10   1   0   0   1   1   0   0   0   0   2

t(as_incidence_matrix(net2)) %*%   as_incidence_matrix(net2)

    U01 U02 U03 U04 U05 U06 U07 U08 U09 U10 U11 U12 U13 U14 U15 U16 U17 U18 U19 U20
U01   2   1   1   0   0   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0
U02   1   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
U03   1   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0
U04   0   0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
U05   0   0   0   1   1   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1
U06   0   0   0   0   0   2   1   1   1   0   0   0   0   0   0   0   0   0   1   1
U07   0   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0   0   0   0
U08   0   0   0   0   0   1   1   1   1   0   0   0   0   0   0   0   0   0   0   0
U09   0   0   0   0   0   1   1   1   2   1   1   0   0   0   0   0   0   0   0   0
U10   0   0   0   0   0   0   0   0   1   1   1   0   0   0   0   0   0   0   0   0
U11   1   0   0   0   0   0   0   0   1   1   3   1   1   0   0   0   0   0   0   0
U12   0   0   0   0   0   0   0   0   0   0   1   1   1   0   0   0   0   0   0   0
U13   0   0   0   0   0   0   0   0   0   0   1   1   2   1   0   0   1   0   0   0
U14   0   0   0   0   0   0   0   0   0   0   0   0   1   2   1   1   1   0   0   0
U15   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1   1   0   0   0   0
U16   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1   2   1   1   1   0
U17   0   0   0   0   0   0   0   0   0   0   0   0   1   1   0   1   2   1   1   0
U18   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   1   1   1   1   0
U19   0   0   0   0   0   1   0   0   0   0   0   0   0   0   0   1   1   1   2   1
U20   0   0   0   1   1   1   0   0   0   0   0   0   0   0   0   0   0   0   1   2

plot(net2.bp$proj1, vertex.label.color="black", vertex.label.dist=1,
     vertex.size=7, vertex.label=nodes2$media[!is.na(nodes2$media.type)])

plot(net2.bp$proj2, vertex.label.color="black", vertex.label.dist=1,
     vertex.size=7, vertex.label=nodes2$media[ is.na(nodes2$media.type)])

5. Plotting networks with igraph Plotting with igraph: the network plots have a wide set of parameters you can set. Those include node options (starting with vertex.) and edge options (starting with edge.). A list of selected options is included below, but you can also check out ?igraph.plotting for more information.

The igraph plotting parameters include (among others):

5.1 Plotting parameters

NODES
vertex.color Node color vertex.frame.color Node border color vertex.shape One of “none”, “circle”, “square”, “csquare”, “rectangle” “crectangle”, “vrectangle”, “pie”, “raster”, or “sphere” vertex.size Size of the node (default is 15) vertex.size2 The second size of the node (e.g. for a rectangle) vertex.label Character vector used to label the nodes vertex.label.family Font family of the label (e.g.“Times”, “Helvetica”) vertex.label.font Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol vertex.label.cex Font size (multiplication factor, device-dependent) vertex.label.dist Distance between the label and the vertex vertex.label.degree The position of the label in relation to the vertex, where 0 right, “pi” is left, “pi/2” is below, and “-pi/2” is above

EDGES
edge.color Edge color edge.width Edge width, defaults to 1 edge.arrow.size Arrow size, defaults to 1 edge.arrow.width Arrow width, defaults to 1 edge.lty Line type, could be 0 or “blank”, 1 or “solid”, 2 or “dashed”, 3 or “dotted”, 4 or “dotdash”, 5 or “longdash”, 6 or “twodash” edge.label Character vector used to label edges edge.label.family Font family of the label (e.g.“Times”, “Helvetica”) edge.label.font Font: 1 plain, 2 bold, 3, italic, 4 bold italic, 5 symbol edge.label.cex Font size for edge labels edge.curved Edge curvature, range 0-1 (FALSE sets it to 0, TRUE to 0.5) arrow.mode Vector specifying whether edges should have arrows, possible values: 0 no arrow, 1 back, 2 forward, 3 both

OTHER
margin Empty space margins around the plot, vector with length 4 frame if TRUE, the plot will be framed main If set, adds a title to the plot sub If set, adds a subtitle to the plot

We can set the node & edge options in two ways - the first one is to specify them in the plot() function, as we are doing below.

# Set edge color to gray, and the node color to orange. 
# Replace the vertex label with the node names stored in "media"
plot(net, edge.arrow.size=.2, edge.curved=0,
     vertex.color="orange", vertex.frame.color="#555555",
     vertex.label=V(net)$media, vertex.label.color="black",
     vertex.label.cex=.7) 

The second way to set attributes is to add them to the igraph object. Let’s say we want to color our network nodes based on type of media, and size them based on audience size (larger audience -> larger node). We will also change the width of the edges based on their weight.

# Generate colors based on media type:
colrs <- c("gray50", "tomato", "gold")
V(net)$color <- colrs[V(net)$media.type]
# Set node size based on audience size:
V(net)$size <- V(net)$audience.size*0.7
# The labels are currently node IDs.
# Setting them to NA will render no labels:
V(net)$label.color <- "black"
V(net)$label <- NA
# Set edge width based on weight:
E(net)$width <- E(net)$weight/6
#change arrow size and edge color:
E(net)$arrow.size <- .2
E(net)$edge.color <- "gray80"
E(net)$width <- 1+E(net)$weight/12
plot(net)

We can also override the attributes explicitly in the plot:

plot(net, edge.color="orange", vertex.color="gray50") 

It helps to add a legend explaining the meaning of the colors we used:

plot(net) 
legend(x=-1.5, y=-1.1, c("Newspaper","Television", "Online News"), pch=21,
       col="#777777", pt.bg=colrs, pt.cex=2, cex=.8, bty="n", ncol=1)

Sometimes, especially with semantic networks, we may be interested in plotting only the labels of the nodes:

plot(net, vertex.shape="none", vertex.label=V(net)$media, 
     vertex.label.font=2, vertex.label.color="gray40",
     vertex.label.cex=.7, edge.color="gray85")

Let’s color the edges of the graph based on their source node color. We can get the starting node for each edge with the ends() igraph function.

edge.start <- ends(net, es=E(net), names=F)[,1]
edge.col <- V(net)$color[edge.start]
plot(net, edge.color=edge.col, edge.curved=.2)  

5.2 Network layouts

Network layouts are simply algorithms that return coordinates for each node in a network.

For the purposes of exploring layouts, we will generate a slightly larger 80-node graph. We use the sample_pa() function which generates a simple graph starting from one node and adding more nodes and links based on a preset level of preferential attachment (Barabasi-Albert model).

net.bg <- sample_pa(80) 
V(net.bg)$size <- 8
V(net.bg)$frame.color <- "white"
V(net.bg)$color <- "orange"
V(net.bg)$label <- "" 
E(net.bg)$arrow.mode <- 0
plot(net.bg)

You can set the layout in the plot function:

plot(net.bg, layout=layout_randomly)

Or you can calculate the vertex coordinates in advance:

l <- layout_in_circle(net.bg)
plot(net.bg, layout=l)

l is simply a matrix of x, y coordinates (N x 2) for the N nodes in the graph. You can easily generate your own:

l <- cbind(1:vcount(net.bg), c(1, vcount(net.bg):2))
plot(net.bg, layout=l)

This layout is just an example and not very helpful - thankfully igraph has a number of built-in layouts, including:

# 3D sphere layout
l <- layout_on_sphere(net.bg)
plot(net.bg, layout=l)

Fruchterman-Reingold is one of the most used force-directed layout algorithms out there.

Force-directed layouts try to get a nice-looking graph where edges are similar in length and cross each other as little as possible. They simulate the graph as a physical system. Nodes are electrically charged particles that repulse each other when they get too close. The edges act as springs that attract connected nodes closer together. As a result, nodes are evenly distributed through the chart area, and the layout is intuitive in that nodes which share more connections are closer to each other. The disadvantage of these algorithms is that they are rather slow and therefore less often used in graphs larger than ~1000 vertices. You can set the “weight” parameter which increases the attraction forces among nodes connected by heavier edges.

l <- layout_with_fr(net.bg)
plot(net.bg, layout=l)

You will notice that the layout is not deterministic - different runs will result in slightly different configurations. Saving the layout in l allows us to get the exact same result multiple times, which can be helpful if you want to plot the time evolution of a graph, or different relationships - and want nodes to stay in the same place in multiple plots.

par(mfrow=c(2,2), mar=c(0,0,0,0))   # plot four figures - 2 rows, 2 columns
plot(net.bg, layout=layout_with_fr)
plot(net.bg, layout=layout_with_fr)

plot(net.bg, layout=l)
plot(net.bg, layout=l)

By default, the coordinates of the plots are rescaled to the [-1,1] interval for both x and y. You can change that with the parameter rescale=FALSE and rescale your plot manually by multiplying the coordinates by a scalar. You can use norm_coords to normalize the plot with the boundaries you want.

l <- layout_with_fr(net.bg)
l <- norm_coords(l, ymin=-1, ymax=1, xmin=-1, xmax=1)
par(mfrow=c(2,2), mar=c(0,0,0,0))
plot(net.bg, rescale=F, layout=l*0.4)
plot(net.bg, rescale=F, layout=l*0.6)

plot(net.bg, rescale=F, layout=l*0.8)
plot(net.bg, rescale=F, layout=l*1.0)

Another popular force-directed algorithm that produces nice results for connected graphs is Kamada Kawai. Like Fruchterman Reingold, it attempts to minimize the energy in a spring system.

l <- layout_with_kk(net.bg)
plot(net.bg, layout=l)

The LGL algorithm is meant for large, connected graphs. Here you can also specify a root: a node that will be placed in the middle of the layout.

plot(net.bg, layout=layout_with_lgl)

Let’s take a look at all available layouts in igraph:

layouts <- grep("^layout_", ls("package:igraph"), value=TRUE)[-1] 
# Remove layouts that do not apply to our graph.
layouts <- layouts[!grepl("bipartite|merge|norm|sugiyama|tree", layouts)]
par(mfrow=c(3,3), mar=c(1,1,1,1))
for (layout in layouts) {
  print(layout)
  l <- do.call(layout, list(net)) 
  plot(net, edge.arrow.mode=0, layout=l, main=layout) }

[1] "layout_as_star"
[1] "layout_components"
[1] "layout_in_circle"
[1] "layout_nicely"
[1] "layout_on_grid"
[1] "layout_on_sphere"
[1] "layout_randomly"
[1] "layout_with_dh"
[1] "layout_with_drl"
[1] "layout_with_fr"

[1] "layout_with_gem"
[1] "layout_with_graphopt"
[1] "layout_with_kk"
[1] "layout_with_lgl"
[1] "layout_with_mds"

5.3 Improving network plots Notice that our network plot is still not too helpful. We can identify the type and size of nodes, but cannot see much about the structure since the links we’re examining are so dense. One way to approach this is to see if we can sparsify the network, keeping only the most important ties and discarding the rest.

hist(links$weight)

mean(links$weight)

[1] 12.40816

sd(links$weight)

[1] 9.905635

There are more sophisticated ways to extract the key edges, but for the purposes of this exercise we’ll only keep ones that have weight higher than the mean for the network. In igraph, we can delete edges using delete_edges(net, edges):

cut.off <- mean(links$weight)
net.sp <- delete_edges(net, E(net)[weight<cut.off])
plot(net.sp) 

Another way to think about this is to plot the two tie types (hyperlink & mention) separately.

E(net)$width <- 1.5
plot(net, edge.color=c("dark red", "slategrey")[(E(net)$type=="hyperlink")+1],
      vertex.color="gray40", layout=layout.circle)

net.m <- net - E(net)[E(net)$type=="hyperlink"] # another way to delete edges
net.h <- net - E(net)[E(net)$type=="mention"]
# Plot the two links separately:
par(mfrow=c(1,2))
plot(net.h, vertex.color="orange", main="Tie: Hyperlink")
plot(net.m, vertex.color="lightsteelblue2", main="Tie: Mention")

# Make sure the nodes stay in place in both plots:
l <- layout_with_fr(net)
plot(net.h, vertex.color="orange", layout=l, main="Tie: Hyperlink")

plot(net.m, vertex.color="lightsteelblue2", layout=l, main="Tie: Mention")

5.4 Interactive plotting with tkplot

R and igraph allow for interactive plotting of networks. This might be a useful option for you if you want to tweak slightly the layout of a small graph. After adjusting the layout manually, you can get the coordinates of the nodes and use them for other plots.

tkid <- tkplot(net) #tkid is the id of the tkplot that will open
l <- tkplot.getcoords(tkid) # grab the coordinates from tkplot
tk_close(tkid, window.close = T)
plot(net, layout=l)

5.5 Other ways to represent a network

At this point it might be useful to provide a quick reminder that there are many ways to represent a network not limited to a hairball plot.

For example, here is a quick heatmap of the network matrix:

netm <- get.adjacency(net, attr="weight", sparse=F)
colnames(netm) <- V(net)$media
rownames(netm) <- V(net)$media
palf <- colorRampPalette(c("gold", "dark orange")) 
heatmap(netm[,17:1], Rowv = NA, Colv = NA, col = palf(100), 
        scale="none", margins=c(10,10) )

5.6 Plotting two-mode networks with igraph

As with one-mode networks, we can modify the network object to include the visual properties that will be used by default when plotting the network. Notice that this time we will also change the shape of the nodes - media outlets will be squares, and their users will be circles.

V(net2)$color <- c("steel blue", "orange")[V(net2)$type+1]
V(net2)$shape <- c("square", "circle")[V(net2)$type+1]
V(net2)$label <- ""
V(net2)$label[V(net2)$type==F] <- nodes2$media[V(net2)$type==F] 
V(net2)$label.cex=.4
V(net2)$label.font=2
plot(net2, vertex.label.color="white", vertex.size=(2-V(net2)$type)*8) 

Igraph also has a special layout for bipartite networks (though it doesn’t always work great, and you might be better off generating your own two-mode layout).

plot(net2, vertex.label=NA, vertex.size=7, layout=layout_as_bipartite) 

Using text as nodes may be helpful at times:

plot(net2, vertex.shape="none", vertex.label=nodes2$media,
     vertex.label.color=V(net2)$color, vertex.label.font=2.5,
     vertex.label.cex=.6, edge.color="gray70",  edge.width=2)

6. Network and node descriptives 6.1 Density

The proportion of present edges from all possible edges in the network.

edge_density(net, loops=F)

[1] 0.1764706

ecount(net)/(vcount(net)*(vcount(net)-1)) #for a directed network

[1] 0.1764706

6.2 Reciprocity

The proportion of reciprocated ties (for a directed network).

reciprocity(net)

[1] 0.4166667

dyad_census(net) # Mutual, asymmetric, and nyll node pairs

$mut
[1] 10

$asym
[1] 28

$null
[1] 98

2*dyad_census(net)$mut/ecount(net) # Calculating reciprocity

[1] 0.4166667

6.3 Transitivity

global - ratio of triangles (direction disregarded) to connected triples. local - ratio of triangles to connected triples each vertex is part of.

transitivity(net, type="global")  # net is treated as an undirected network

[1] 0.372549

transitivity(as.undirected(net, mode="collapse")) # same as above

[1] 0.372549

transitivity(net, type="local")

 [1] 0.2142857 0.4000000 0.1153846 0.1944444 0.5000000 0.2666667 0.2000000 0.1000000
 [9] 0.3333333 0.3000000 0.3333333 0.2000000 0.1666667 0.1666667 0.3000000 0.3333333
[17] 0.2000000

triad_census(net) # for directed networks 

 [1] 244 241  80  13  11  27  15  22   4   1   8   4   4   3   3   0

Triad types (per Davis & Leinhardt):

003 A, B, C, empty triad. 012 A->B, C 102 A<->B, C 021D A<-B->C 021U A->B<-C 021C A->B->C 111D A<->B<-C 111U A<->B->C 030T A->B<-C, A->C 030C A<-B<-C, A->C. 201 A<->B<->C. 120D A<-B->C, A<->C. 120U A->B<-C, A<->C. 120C A->B->C, A<->C. 210 A->B<->C, A<->C. 300 A<->B<->C, A<->C, completely connected. 6.4 Diameter

A network diameter is the longest geodesic distance (length of the shortest path between two nodes) in the network. In igraph, diameter() returns the distance, while get_diameter() returns the nodes along the first found path of that distance.

Note that edge weights are used by default, unless set to NA.

diameter(net, directed=F, weights=NA)

[1] 4

diameter(net, directed=F)

[1] 28

diam <- get_diameter(net, directed=T)
diam

+ 7/17 vertices, named, from b90c4f0:
[1] s12 s06 s17 s04 s03 s08 s07

Note that get_diameter() returns a vertex sequence. Note though that when asked to behaved as a vector, a vertex sequence will produce the numeric indexes of the nodes in it. The same applies for edge sequences.

class(diam)

[1] "igraph.vs"

Color nodes along the diameter:

vcol <- rep("gray40", vcount(net))
vcol[diam] <- "gold"
ecol <- rep("gray80", ecount(net))
ecol[E(net, path=diam)] <- "orange" 
# E(net, path=diam) finds edges along a path, here 'diam'
plot(net, vertex.color=vcol, edge.color=ecol, edge.arrow.mode=0)

6.5 Node degrees

The function degree() has a mode of in for in-degree, out for out-degree, and all or total for total degree.

deg <- degree(net, mode="all")
plot(net, vertex.size=deg*3)

hist(deg, breaks=1:vcount(net)-1, main="Histogram of node degree")

6.6 Degree distribution

deg.dist <- degree_distribution(net, cumulative=T, mode="all")
plot( x=0:max(deg), y=1-deg.dist, pch=19, cex=1.2, col="orange", 
      xlab="Degree", ylab="Cumulative Frequency")

6.7 Centrality & centralization

Centrality functions (vertex level) and centralization functions (graph level). The centralization functions return res - vertex centrality, centralization, and theoretical_max - maximum centralization score for a graph of that size. The centrality function can run on a subset of nodes (set with the vids parameter). This is helpful for large graphs where calculating all centralities may be a resource-intensive and time-consuming task.

Degree (number of ties)

degree(net, mode="in")

s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17 
  4   2   6   4   1   4   1   2   3   4   3   3   2   2   2   1   4 

centr_degree(net, mode="in", normalized=T)

$res
 [1] 4 2 6 4 1 4 1 2 3 4 3 3 2 2 2 1 4

$centralization
[1] 0.1985294

$theoretical_max
[1] 272

Closeness (centrality based on distance to others in the graph) Inverse of the node’s average geodesic distance to others in the network.

closeness(net, mode="all", weights=NA)

       s01        s02        s03        s04        s05        s06        s07        s08 
0.03333333 0.03030303 0.04166667 0.03846154 0.03225806 0.03125000 0.03030303 0.02857143 
       s09        s10        s11        s12        s13        s14        s15        s16 
0.02564103 0.02941176 0.03225806 0.03571429 0.02702703 0.02941176 0.03030303 0.02222222 
       s17 
0.02857143 

centr_clo(net, mode="all", normalized=T) 

$res
 [1] 0.5333333 0.4848485 0.6666667 0.6153846 0.5161290 0.5000000 0.4848485 0.4571429
 [9] 0.4102564 0.4705882 0.5161290 0.5714286 0.4324324 0.4705882 0.4848485 0.3555556
[17] 0.4571429

$centralization
[1] 0.3753596

$theoretical_max
[1] 7.741935

Eigenvector (centrality proportional to the sum of connection centralities) Values of the first eigenvector of the graph matrix.

eigen_centrality(net, directed=T, weights=NA)

$vector
      s01       s02       s03       s04       s05       s06       s07       s08 
0.6638179 0.3314674 1.0000000 0.9133129 0.3326443 0.7468249 0.1244195 0.3740317 
      s09       s10       s11       s12       s13       s14       s15       s16 
0.3453324 0.5991652 0.7334202 0.7519086 0.3470857 0.2915055 0.3314674 0.2484270 
      s17 
0.7503292 

$value
[1] 3.006215

$options
$options$bmat
[1] "I"

$options$n
[1] 17

$options$which
[1] "LR"

$options$nev
[1] 1

$options$tol
[1] 0

$options$ncv
[1] 0

$options$ldv
[1] 0

$options$ishift
[1] 1

$options$maxiter
[1] 1000

$options$nb
[1] 1

$options$mode
[1] 1

$options$start
[1] 1

$options$sigma
[1] 0

$options$sigmai
[1] 0

$options$info
[1] 0

$options$iter
[1] 7

$options$nconv
[1] 1

$options$numop
[1] 31

$options$numopb
[1] 0

$options$numreo
[1] 18

centr_eigen(net, directed=T, normalized=T) 

$vector
 [1] 0.6638179 0.3314674 1.0000000 0.9133129 0.3326443 0.7468249 0.1244195 0.3740317
 [9] 0.3453324 0.5991652 0.7334202 0.7519086 0.3470857 0.2915055 0.3314674 0.2484270
[17] 0.7503292

$value
[1] 3.006215

$options
$options$bmat
[1] "I"

$options$n
[1] 17

$options$which
[1] "LR"

$options$nev
[1] 1

$options$tol
[1] 0

$options$ncv
[1] 0

$options$ldv
[1] 0

$options$ishift
[1] 1

$options$maxiter
[1] 1000

$options$nb
[1] 1

$options$mode
[1] 1

$options$start
[1] 1

$options$sigma
[1] 0

$options$sigmai
[1] 0

$options$info
[1] 0

$options$iter
[1] 7

$options$nconv
[1] 1

$options$numop
[1] 31

$options$numopb
[1] 0

$options$numreo
[1] 18


$centralization
[1] 0.5071775

$theoretical_max
[1] 16

Betweenness (centrality based on a broker position connecting others) Number of geodesics that pass through the node or the edge.

betweenness(net, directed=T, weights=NA)

        s01         s02         s03         s04         s05         s06         s07 
 24.0000000   5.8333333 127.0000000  93.5000000  16.5000000  20.3333333   1.8333333 
        s08         s09         s10         s11         s12         s13         s14 
 19.5000000   0.8333333  15.0000000   0.0000000  33.5000000  20.0000000   4.0000000 
        s15         s16         s17 
  5.6666667   0.0000000  58.5000000 

edge_betweenness(net, directed=T, weights=NA)

 [1] 10.833333 11.333333  8.333333  9.500000  4.000000 12.500000  3.000000  2.333333
 [9] 24.000000 16.000000 31.500000 32.500000  9.500000  6.500000 23.000000 65.333333
[17] 11.000000  6.500000 18.000000  8.666667  5.333333 10.000000  6.000000 11.166667
[25] 15.000000 21.333333 10.000000  2.000000  1.333333  4.500000 11.833333 16.833333
[33]  6.833333 16.833333 31.000000 17.000000 18.000000 14.500000  7.500000 28.500000
[41]  3.000000 17.000000  5.666667  9.666667  6.333333  1.000000 15.000000 74.500000

centr_betw(net, directed=T, normalized=T)

$res
 [1]  24.0000000   5.8333333 127.0000000  93.5000000  16.5000000  20.3333333   1.8333333
 [8]  19.5000000   0.8333333  15.0000000   0.0000000  33.5000000  20.0000000   4.0000000
[15]   5.6666667   0.0000000  58.5000000

$centralization
[1] 0.4460938

$theoretical_max
[1] 3840

6.8 Hubs and authorities

The hubs and authorities algorithm developed by Jon Kleinberg was initially used to examine web pages. Hubs were expected to contain catalogs with a large number of outgoing links; while authorities would get many incoming links from hubs, presumably because of their high-quality relevant information.

hs <- hub_score(net, weights = NA)$vector
as <- authority_score(net, weights = NA)$vector
par(mfrow = c(1,2))
 plot(net, vertex.size = hs*50, main = "Hubs")
 plot(net, vertex.size = as*30, main = "Authorities")

7. Distances and paths Average path length: the mean of the shortest distance between each pair of nodes in the network (in both directions for directed graphs).

mean_distance(net, directed=F)

[1] 2.058824

mean_distance(net, directed=T)

[1] 2.742188

We can also find the length of all shortest paths in the graph:

distances(net) # with edge weights

    s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17
s01   0   4   2   6   1   5   3   4   3   4   3   3   9   4   7  26   8
s02   4   0   4   8   3   7   5   6   1   5   5   5  11   6   9  28  10
s03   2   4   0   4   1   3   1   2   3   2   1   1   7   2   5  24   6
s04   6   8   4   0   5   1   5   6   7   6   5   3   3   6   1  22   2
s05   1   3   1   5   0   4   2   3   2   3   2   2   8   3   6  25   7
s06   5   7   3   1   4   0   4   5   6   5   4   2   4   5   2  21   3
s07   3   5   1   5   2   4   0   3   4   3   2   2   8   3   6  25   7
s08   4   6   2   6   3   5   3   0   5   4   3   3   9   4   7  26   8
s09   3   1   3   7   2   6   4   5   0   5   4   4  10   5   8  27   9
s10   4   5   2   6   3   5   3   4   5   0   3   3   9   4   7  26   8
s11   3   5   1   5   2   4   2   3   4   3   0   2   8   1   6  25   7
s12   3   5   1   3   2   2   2   3   4   3   2   0   6   3   4  23   5
s13   9  11   7   3   8   4   8   9  10   9   8   6   0   9   4  22   1
s14   4   6   2   6   3   5   3   4   5   4   1   3   9   0   7  26   8
s15   7   9   5   1   6   2   6   7   8   7   6   4   4   7   0  23   3
s16  26  28  24  22  25  21  25  26  27  26  25  23  22  26  23   0  21
s17   8  10   6   2   7   3   7   8   9   8   7   5   1   8   3  21   0

distances(net, weights=NA) # ignore weights

    s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17
s01   0   1   1   1   1   2   2   2   2   2   2   2   3   3   1   3   2
s02   1   0   1   2   1   3   2   2   1   1   2   2   3   3   2   4   3
s03   1   1   0   1   1   2   1   1   2   1   1   1   2   2   2   3   2
s04   1   2   1   0   2   1   2   2   3   2   1   1   2   2   1   2   1
s05   1   1   1   2   0   2   2   2   1   2   2   2   3   3   1   3   3
s06   2   3   2   1   2   0   3   3   3   3   2   1   2   2   1   1   1
s07   2   2   1   2   2   3   0   1   2   1   2   2   2   1   3   4   3
s08   2   2   1   2   2   3   1   0   1   2   2   2   3   2   3   4   3
s09   2   1   2   3   1   3   2   1   0   1   3   3   4   3   2   4   4
s10   2   1   1   2   2   3   1   2   1   0   2   2   3   2   3   4   3
s11   2   2   1   1   2   2   2   2   3   2   0   2   2   1   2   3   2
s12   2   2   1   1   2   1   2   2   3   2   2   0   1   1   2   2   2
s13   3   3   2   2   3   2   2   3   4   3   2   1   0   1   3   2   1
s14   3   3   2   2   3   2   1   2   3   2   1   1   1   0   3   3   2
s15   1   2   2   1   1   1   3   3   2   3   2   2   3   3   0   2   2
s16   3   4   3   2   3   1   4   4   4   4   3   2   2   3   2   0   1
s17   2   3   2   1   3   1   3   3   4   3   2   2   1   2   2   1   0

We can extract the distances to a node or set of nodes we are interested in. Here we will get the distance of every media from the New York Times.

dist.from.NYT <- distances(net, v=V(net)[media == "NY Times"], to=V(net), weights=NA)
# Set colors to plot the distances:
oranges <- colorRampPalette(c("dark red", "gold"))
col <- oranges(max(dist.from.NYT)+1)
col <- col[dist.from.NYT+1]
plot(net, vertex.color=col, vertex.label=dist.from.NYT, edge.arrow.size=.6, 
     vertex.label.color="white")

We can also find the shortest path between specific nodes. Say here between MSNBC and the New York Post: (using the shortest_path)

news.path <- shortest_paths(net, from = V(net)[media=="MSNBC"], 
                             to  = V(net)[media=="New York Post"],
                             output = "both") # both path nodes and edges
# Generate edge color variable to plot the path:
ecol <- rep("gray80", ecount(net))
ecol[unlist(news.path$epath)] <- "orange"
# Generate edge width variable to plot the path:
ew <- rep(2, ecount(net))
ew[unlist(news.path$epath)] <- 4
# Generate node color variable to plot the path:
vcol <- rep("gray40", vcount(net))
vcol[unlist(news.path$vpath)] <- "gold"
plot(net, vertex.color=vcol, edge.color=ecol, 
     edge.width=ew, edge.arrow.mode=0)

library(d3Network)
d3SimpleNetwork(links, iframe = T)

<iframe src='NetworkGraph0wKN9.html' height=654 width=945></iframe>

library(visNetwork)
nodes$label = nodes$media
# use igraph to compute useful statistics.
ig = graph_from_data_frame(links, directed = F)
clusters = cluster_edge_betweenness(ig)
nodes$group = clusters$membership
# set nodes sizes as a function of their betweeness
nodes$value = betweenness(ig)
dev.new(width=8, height=6)
visNetwork(nodes, links)