1. Create networks

The code below generates an undirected graph with three edges. The numbers are interpreted as vertex IDs, so the edges are 1->2, 2->3, 3->1.

library(igraph)
## Warning: package 'igraph' was built under R version 3.4.2
## 
## Attaching package: 'igraph'
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## The following object is masked from 'package:base':
## 
##     union
g1 <- graph( edges=c(1,2, 2,3, 3, 1), n=3, directed=F ) 

plot(g1) 

class(g1)
## [1] "igraph"
g1
## IGRAPH 03de446 U--- 3 3 -- 
## + edges from 03de446:
## [1] 1--2 2--3 1--3

Now with 8 vertices, and directed by default:

Name vertices

g3 <- graph( c("Neil", "Claire", "Claire", "Peggie", "Peggie", "Neil")) # 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=0.8, vertex.label.dist=2, edge.curved=0.2)

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))

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, h-e:f:i, j)

plot(gl)

2. Edge, vertex, and network attributes

Access vertices and edges:

E(g4)
## + 4/4 edges from 047a366 (vertex names):
## [1] John->Jim  Jim ->Jack Jim ->Jack John->John
V(g4)
## + 7/7 vertices, named, from 047a366:
## [1] John     Jim      Jack     Jesse    Janis    Jennifer Justin

view network matrix

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)$name # automatically generated when we created the network.t
## [1] "John"     "Jim"      "Jack"     "Jesse"    "Janis"    "Jennifer"
## [7] "Justin"
V(g4)$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"
## [7] "Justin"  
## 
## $gender
## [1] "male"   "male"   "male"   "male"   "female" "female" "male"
graph_attr(g4)
## named list()

Set attributes

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

graph_attr(g4, "name")
## NULL
graph_attr(g4)
## named list()
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 05b7e6c DNW- 7 3 -- 
## + attr: name (v/c), gender (v/c), weight (e/n)
## + edges from 05b7e6c (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

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 = 3, 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=40) 

plot(er, vertex.size=6, 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, m=1,  directed=F)

 plot(ba, vertex.size=6, vertex.label=NA)

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

historical graphs

 zach <- graph("Zachary") # the Zachary carate 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, 5)

 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)