Danilo Martinez Network Science HW #3 & EXTRA Credit
- (20 points) In HW 1, you generated a random network. Now, you will generated a scale-free network using the Barabasi-Albert model that we discussed on 2nd Nov. Submit hardcopy of the program for 1(b).
1(a): Create a network with 4 nodes that are connected to each other i.e., a complete graph with 4 nodes and the degree for all is 3.
library("network")
library(igraph)
n<-4
p.<-1
g<-erdos.renyi.game(n,p.,type = c("gnp"),directed = FALSE,loops = FALSE)
plot.igraph(g)
g## IGRAPH 157681e U--- 4 6 -- Erdos renyi (gnp) graph
## + attr: name (g/c), type (g/c), loops (g/l), p (g/n)
## + edges from 157681e:
## [1] 1--2 1--3 1--4 2--3 2--4 3--4Number of nodes is 4 Number of links is 6
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g,v=V(g), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 3 3 3 3Add a new node (the 5th one) to this existing network such that the new node randomly attaches to 3 nodes of the existing network with probabilities that are proportional to the degrees of the nodes already in the network. Make sure that there are no multiple edges (the same node must not be linked more than once). Now, you have a 5-node network. Update the degrees of all the nodes.
g5<-barabasi.game(5, power = 1, m = 3, out.dist = NULL, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g)
plot.igraph(g5)
g5## IGRAPH 159d372 U--- 5 9 -- Barabasi graph
## + attr: name (g/c), power (g/n), m (g/n), zero.appeal (g/n),
## | algorithm (g/c)
## + edges from 159d372:
## [1] 1--2 1--3 1--4 2--3 2--4 3--4 3--5 1--5 4--5Number of nodes is 5 Number of links is 9
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g5,v=V(g5), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 4 3 4 4 3Add the 6th node (with 3 links) in a similar fashion.
g6<-barabasi.game(6, power = 1, m = 3, out.dist = NULL, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g5)
plot.igraph(g6)
g6## IGRAPH 1653475 U--- 6 12 -- Barabasi graph
## + attr: name (g/c), power (g/n), m (g/n), zero.appeal (g/n),
## | algorithm (g/c)
## + edges from 1653475:
## [1] 1--2 1--3 1--4 2--3 2--4 3--4 3--5 1--5 4--5 1--6 2--6 5--6Number of nodes is 6 Number of links is 12
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g6,v=V(g6), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 5 4 4 4 4 3Continue to add 5000 nodes. The final network has 5004 nodes with (6+15000) links. In the following graph, larger Nodes have a higher degree and are shown in the center.
g5004<-barabasi.game(5004, power = 1, m = 3, out.dist = NULL, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g6)
deg <- degree(g5004, mode="all")
l <- layout_with_fr(g5004)
l <- norm_coords(l, ymin=-15.3, ymax=15.3, xmin=-23, xmax=23)
par(mfrow=c(1,1), mar=c(0,0,0,0))
plot(g5004, rescale=F, layout=l*.07,vertex.label=NA,vertex.size=deg*.1,edge.width=.0000000000000000001,edge.curved=.1)
g5004## IGRAPH 1676296 U--- 5004 15006 -- Barabasi graph
## + attr: name (g/c), power (g/n), m (g/n), zero.appeal (g/n),
## | algorithm (g/c)
## + edges from 1676296:
## [1] 1-- 2 1-- 3 1-- 4 2-- 3 2-- 4 3-- 4 3-- 5 1-- 5 4-- 5 1-- 6
## [11] 2-- 6 5-- 6 2-- 7 5-- 7 6-- 7 2-- 8 4-- 8 1-- 8 2-- 9 7-- 9
## [21] 5-- 9 5--10 2--10 7--10 3--11 6--11 2--11 2--12 6--12 10--12
## [31] 5--13 4--13 11--13 9--14 7--14 1--14 10--15 9--15 4--15 4--16
## [41] 2--16 3--16 1--17 5--17 11--17 12--18 7--18 1--18 2--19 12--19
## [51] 4--19 11--20 14--20 2--20 16--21 12--21 13--21 5--22 16--22 3--22
## [61] 5--23 10--23 2--23 4--24 12--24 5--24 21--25 23--25 3--25 10--26
## + ... omitted several edgesNumber of nodes is 5004 Number of links is 15006
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g5004,v=V(g5004), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 130 137 89 109 150 48 117 67 73 63 61 54 65 41 56 24 56
## [18] 48 51 12 25 39 100 28 24 24 24 27 32 22 25 5 62 36
## [35] 17 26 37 11 20 34 18 34 32 20 51 14 35 17 36 42 25
## [52] 31 32 7 25 32 33 21 18 25 13 23 24 48 14 24 56 37
## [69] 56 37 29 9 25 17 13 27 5 44 43 56 25 31 37 25 10
## [86] 22 22 14 17 21 7 23 57 24 20 35 19 10 29 31 26 19
## [103] 9 13 19 16 16 9 15 30 21 5 17 7 11 18 16 28 37
## [120] 13 20 12 17 12 16 13 24 21 10 15 12 11 13 26 14 15
## [137] 15 23 28 20 25 8 20 17 8 13 22 21 11 16 9 25 10
## [154] 21 26 27 14 9 7 35 7 24 6 7 12 9 5 6 7 16
## [171] 17 17 24 26 16 16 28 17 15 5 16 24 8 16 15 12 16
## [188] 20 33 19 15 11 9 11 6 25 13 18 18 17 25 8 10 5
## [205] 17 12 10 24 12 21 18 13 12 10 6 19 17 15 18 11 6
## [222] 8 7 6 22 7 21 20 25 10 12 16 15 7 23 6 23 8
## [239] 21 14 18 5 18 10 7 15 10 5 12 31 14 48 6 22 8
## [256] 7 14 6 3 7 18 13 9 18 15 10 10 6 18 8 11 16
## [273] 8 15 15 12 22 17 9 7 7 15 8 11 17 21 21 26 25
## [290] 23 8 8 7 9 6 7 27 15 12 20 8 13 14 9 9 11
## [307] 4 4 16 7 26 12 7 14 17 4 8 17 13 10 11 19 7
## [324] 16 18 16 6 23 7 8 7 13 6 6 13 13 4 13 16 10
## [341] 10 10 6 10 8 12 7 9 12 27 12 13 12 10 9 8 18
## [358] 9 10 12 5 14 15 8 10 10 6 9 6 7 4 7 11 13
## [375] 7 12 12 9 4 10 16 7 8 7 17 21 15 13 12 7 20
## [392] 13 12 6 12 12 13 5 12 10 11 11 12 4 3 5 5 6
## [409] 8 8 12 10 22 7 12 9 12 11 13 17 8 15 8 8 15
## [426] 7 9 8 16 10 13 9 19 8 11 16 23 15 10 11 6 14
## [443] 6 8 9 7 12 15 9 13 5 8 11 18 12 6 11 9 7
## [460] 7 12 16 14 10 7 8 11 12 11 8 12 7 7 11 12 9
## [477] 12 8 8 11 28 8 7 12 5 13 10 12 18 11 8 10 9
## [494] 14 12 6 13 5 7 3 5 10 8 10 7 12 15 10 19 13
## [511] 10 10 5 15 16 6 11 5 8 5 14 3 12 16 13 10 10
## [528] 6 8 10 13 11 4 14 6 16 6 6 4 5 12 12 11 9
## [545] 17 5 8 6 5 8 9 9 5 8 12 15 8 7 4 12 10
## [562] 7 6 13 7 7 7 6 7 9 11 5 7 7 15 12 15 7
## [579] 7 7 11 6 9 10 9 8 9 13 5 7 5 17 9 12 12
## [596] 11 10 8 9 8 10 9 6 10 7 8 5 7 10 11 9 10
## [613] 5 19 12 6 9 5 7 9 6 10 11 12 5 7 8 7 7
## [630] 9 7 9 4 8 7 9 6 11 3 10 9 13 7 9 14 8
## [647] 10 7 8 8 8 14 11 7 13 5 10 8 6 7 11 3 7
## [664] 13 3 8 5 6 10 6 22 10 10 4 6 13 8 11 4 11
## [681] 6 8 7 8 9 9 10 9 10 7 9 8 12 8 7 9 9
## [698] 7 5 6 5 11 5 9 15 6 6 9 6 6 9 7 11 9
## [715] 4 4 8 7 3 9 6 8 6 5 6 5 4 13 5 10 9
## [732] 14 7 8 9 10 4 14 7 8 3 4 6 15 4 12 5 14
## [749] 20 6 13 9 3 6 7 9 6 11 6 9 12 6 7 5 6
## [766] 12 6 13 7 12 12 3 5 5 8 15 6 5 9 4 4 5
## [783] 7 6 5 4 4 6 8 7 8 11 9 11 13 8 11 5 8
## [800] 4 10 8 6 5 14 5 12 9 8 9 7 10 12 7 6 9
## [817] 12 13 5 6 4 8 7 10 5 4 8 7 5 9 7 15 9
## [834] 10 4 11 11 7 18 3 3 11 8 13 6 6 4 14 7 4
## [851] 9 5 6 21 6 8 9 4 5 9 4 8 10 6 10 10 5
## [868] 7 6 8 8 9 6 4 4 8 12 11 8 9 6 4 5 6
## [885] 8 8 9 5 10 7 6 6 6 12 4 10 15 3 11 5 3
## [902] 6 7 4 4 6 6 8 8 3 13 4 8 13 5 11 9 8
## [919] 10 4 5 8 8 5 5 6 5 9 7 12 7 5 11 12 11
## [936] 7 8 6 7 8 8 4 6 6 6 5 5 8 8 5 8 6
## [953] 6 5 7 6 4 4 13 5 6 4 6 3 4 7 13 11 7
## [970] 6 7 9 6 6 6 4 7 7 10 8 8 4 4 10 9 7
## [987] 6 8 7 6 5 3 3 6 7 6 12 10 11 8 8 11 6
## [1004] 7 6 6 6 8 6 8 5 13 10 3 8 5 9 4 10 8
## [1021] 11 3 6 8 12 4 5 5 12 6 3 8 8 6 4 10 11
## [1038] 8 5 6 9 6 7 6 8 6 11 10 6 3 7 8 11 5
## [1055] 6 7 12 5 10 8 5 3 6 8 7 10 7 6 3 7 6
## [1072] 8 6 6 4 11 10 3 7 7 6 8 6 8 7 9 10 7
## [1089] 9 6 10 4 3 5 10 6 4 10 6 6 10 4 6 9 6
## [1106] 4 6 3 9 5 7 10 5 6 12 3 5 4 6 6 14 7
## [1123] 6 12 3 10 6 7 4 5 8 11 7 8 4 4 7 5 5
## [1140] 7 5 11 7 7 6 5 5 4 6 9 9 6 10 8 4 8
## [1157] 6 9 10 7 5 8 6 5 7 12 3 8 5 5 15 3 10
## [1174] 3 5 11 7 10 8 8 6 3 10 6 5 4 6 8 13 5
## [1191] 5 5 3 5 3 6 12 5 3 4 3 5 7 9 9 7 4
## [1208] 8 6 3 7 7 7 5 11 3 6 6 6 14 8 5 4 3
## [1225] 4 6 5 6 5 5 7 4 7 7 7 5 6 8 6 3 5
## [1242] 5 5 5 8 3 4 4 9 6 5 8 6 8 4 9 10 5
## [1259] 5 4 6 5 7 9 6 8 5 5 9 4 9 5 5 3 6
## [1276] 5 4 10 7 5 5 7 7 5 8 4 5 10 5 6 3 6
## [1293] 5 6 8 4 6 9 4 4 4 8 7 5 7 7 8 4 7
## [1310] 7 7 3 8 10 5 4 4 5 8 4 4 4 5 4 5 7
## [1327] 6 4 4 4 4 7 9 7 7 6 3 7 4 9 11 8 4
## [1344] 9 5 8 4 4 5 4 7 5 7 6 6 6 4 3 7 9
## [1361] 6 4 4 12 4 7 5 9 6 4 6 11 6 6 4 6 4
## [1378] 5 12 5 8 3 5 3 4 4 4 5 6 6 4 4 6 6
## [1395] 4 5 6 8 8 10 5 3 5 10 8 5 7 3 8 5 9
## [1412] 4 3 5 3 4 8 9 8 5 4 5 9 10 5 5 6 5
## [1429] 3 12 6 3 3 6 7 6 5 14 9 7 4 11 5 3 6
## [1446] 7 8 5 7 6 5 5 4 4 6 8 6 6 4 9 4 4
## [1463] 18 4 6 7 6 7 7 7 8 7 3 4 5 5 6 5 5
## [1480] 5 6 6 4 6 4 6 3 12 5 5 9 5 6 3 7 6
## [1497] 7 7 8 3 3 4 4 13 6 9 6 9 5 4 3 4 3
## [1514] 5 3 11 4 9 4 4 5 6 3 11 5 5 6 7 3 4
## [1531] 4 5 8 5 9 5 6 4 6 5 7 5 8 7 5 7 3
## [1548] 5 4 4 8 11 6 5 4 5 4 8 4 5 4 3 7 4
## [1565] 3 5 7 4 5 4 5 6 4 9 4 3 6 6 8 8 3
## [1582] 5 8 3 6 3 5 9 4 8 8 5 6 5 3 7 4 4
## [1599] 5 6 6 5 5 8 8 5 3 4 7 10 10 6 5 9 6
## [1616] 3 6 9 8 5 5 4 5 6 8 5 6 7 5 3 4 6
## [1633] 6 6 3 4 9 4 7 3 6 6 7 4 6 3 4 7 4
## [1650] 5 6 8 6 5 4 7 3 5 9 7 7 5 4 4 4 5
## [1667] 5 5 4 6 4 4 3 10 7 3 6 6 6 3 6 4 6
## [1684] 4 6 7 5 4 5 4 8 6 5 3 5 4 7 3 3 9
## [1701] 6 3 3 6 6 4 5 7 4 4 5 4 5 5 3 6 5
## [1718] 5 5 5 10 6 5 7 4 6 3 5 3 10 4 7 5 7
## [1735] 3 5 4 4 5 4 6 4 6 7 5 9 6 10 7 3 3
## [1752] 7 7 4 4 5 5 6 5 3 6 4 5 5 3 6 7 3
## [1769] 5 6 3 3 10 6 6 4 8 5 6 3 4 4 3 4 7
## [1786] 6 7 6 8 4 4 3 6 9 3 4 5 4 4 4 6 8
## [1803] 5 7 5 5 3 4 6 4 6 5 4 6 3 4 6 4 4
## [1820] 3 8 4 5 4 4 5 4 4 5 5 4 4 6 6 7 4
## [1837] 5 6 5 4 4 4 5 6 8 5 8 9 4 3 4 4 4
## [1854] 5 4 3 3 4 4 6 5 5 5 5 4 5 8 5 6 5
## [1871] 3 7 4 6 4 3 7 6 8 4 6 3 5 5 3 4 5
## [1888] 4 6 9 3 5 3 4 5 5 3 3 7 7 6 4 5 3
## [1905] 4 7 4 6 4 4 8 5 5 3 3 6 5 3 7 4 6
## [1922] 11 8 3 3 4 7 5 3 6 8 6 7 6 5 8 4 4
## [1939] 3 6 4 4 4 6 10 3 3 3 5 3 4 5 6 7 4
## [1956] 3 9 6 9 10 4 6 3 7 5 6 3 4 4 5 4 5
## [1973] 7 5 6 7 6 5 5 5 6 7 5 8 4 3 5 8 4
## [1990] 3 5 5 7 4 4 3 5 5 5 4 4 6 3 5 9 4
## [2007] 7 6 6 5 3 3 5 7 3 3 4 4 5 6 6 6 3
## [2024] 3 3 7 9 3 3 4 5 7 5 5 6 3 4 4 4 4
## [2041] 4 5 4 4 5 3 3 5 3 7 5 5 4 7 3 9 5
## [2058] 5 6 3 3 3 3 8 4 5 6 3 4 3 8 8 4 4
## [2075] 5 3 4 4 5 7 5 6 4 4 5 6 7 11 6 3 8
## [2092] 5 4 4 4 6 3 3 6 4 5 4 10 4 4 5 3 4
## [2109] 9 8 4 6 5 3 3 4 4 3 3 6 4 4 3 7 5
## [2126] 3 3 5 5 6 7 3 3 5 3 5 9 8 3 5 6 7
## [2143] 4 4 5 4 5 6 6 4 6 3 5 7 6 7 5 3 3
## [2160] 3 6 13 6 7 4 5 9 3 10 3 4 7 6 4 7 3
## [2177] 4 5 5 7 3 6 4 3 4 6 3 5 3 12 6 4 5
## [2194] 4 4 4 5 6 4 4 4 4 3 4 5 3 4 3 5 3
## [2211] 4 5 5 6 6 3 5 4 4 4 4 4 4 3 3 6 3
## [2228] 4 6 5 3 3 3 5 3 3 3 5 3 4 6 6 9 6
## [2245] 3 3 6 3 6 7 7 3 5 6 6 4 6 5 4 6 6
## [2262] 3 4 4 4 4 5 3 8 3 5 5 3 4 4 3 3 5
## [2279] 10 4 3 8 4 4 4 3 8 3 5 6 4 6 4 4 10
## [2296] 3 4 3 4 4 6 3 3 4 6 3 5 5 4 8 5 4
## [2313] 7 3 3 7 6 3 4 6 3 6 3 3 11 6 8 5 4
## [2330] 4 5 5 6 4 6 6 5 3 5 5 3 5 5 4 3 4
## [2347] 7 7 3 6 3 6 4 3 3 3 7 6 4 4 3 6 5
## [2364] 4 4 4 3 4 6 4 3 6 3 4 7 5 7 5 3 3
## [2381] 4 6 4 7 7 5 4 5 4 5 3 4 4 6 3 3 6
## [2398] 3 4 3 4 5 3 3 4 9 4 3 4 5 3 6 4 6
## [2415] 4 4 4 6 4 7 3 8 6 4 6 4 5 4 3 3 6
## [2432] 4 5 4 8 3 6 4 4 4 4 4 7 8 5 7 3 3
## [2449] 4 3 3 8 3 4 5 4 3 5 4 6 5 5 3 6 4
## [2466] 5 3 3 3 5 4 5 5 4 3 3 5 4 6 6 3 7
## [2483] 4 3 6 5 4 5 5 5 3 4 3 3 4 7 3 4 7
## [2500] 6 6 5 8 4 5 3 5 4 7 4 4 4 3 4 3 3
## [2517] 3 5 3 7 3 5 3 6 5 4 6 4 4 5 4 6 4
## [2534] 3 8 3 4 5 3 6 3 3 5 6 3 8 4 4 3 4
## [2551] 4 5 6 6 3 8 4 6 3 3 7 3 3 6 4 4 4
## [2568] 5 4 3 4 3 5 5 5 5 3 3 3 3 3 5 4 5
## [2585] 4 4 5 6 4 5 7 3 4 6 3 3 3 4 4 4 6
## [2602] 6 3 4 3 3 4 6 4 7 3 5 3 4 5 5 4 6
## [2619] 5 4 4 5 4 4 4 4 9 3 5 5 5 3 3 3 3
## [2636] 4 3 4 4 3 4 3 3 5 3 5 4 4 5 4 5 6
## [2653] 3 3 3 6 4 3 5 5 4 3 4 4 4 3 5 3 3
## [2670] 4 4 3 4 3 4 4 3 5 4 3 3 4 4 3 3 4
## [2687] 3 4 5 6 4 4 3 4 3 3 4 4 4 5 6 8 3
## [2704] 3 3 4 5 4 3 4 5 3 4 4 3 3 3 3 4 5
## [2721] 3 5 3 6 6 5 3 6 3 3 4 4 3 6 6 4 4
## [2738] 4 3 4 3 6 5 4 3 5 4 3 5 3 3 3 4 3
## [2755] 5 4 6 4 3 4 4 3 5 3 4 4 6 6 3 3 3
## [2772] 3 4 4 3 3 5 4 5 5 6 4 4 5 4 4 4 4
## [2789] 4 5 5 5 4 5 5 3 3 3 4 3 5 4 4 4 3
## [2806] 3 7 3 3 4 6 3 4 4 4 3 6 5 3 8 7 4
## [2823] 3 4 3 4 4 3 4 3 3 5 4 3 6 3 5 5 5
## [2840] 4 3 5 5 5 4 3 3 3 3 3 3 5 4 3 5 3
## [2857] 3 3 3 3 3 4 3 5 3 4 4 6 4 4 3 3 3
## [2874] 5 4 3 6 4 4 4 4 3 4 4 5 4 4 3 4 3
## [2891] 7 4 3 4 4 5 5 4 3 3 3 3 3 5 3 3 4
## [2908] 5 4 3 3 4 5 6 3 3 4 7 3 3 3 5 3 5
## [2925] 3 3 3 3 4 3 3 6 6 3 12 5 4 3 4 3 3
## [2942] 4 4 3 4 6 3 3 3 6 6 4 3 4 4 3 3 3
## [2959] 5 5 4 3 3 3 4 6 5 3 3 3 4 5 4 9 5
## [2976] 3 4 7 4 6 4 3 3 6 6 5 3 3 3 4 4 4
## [2993] 4 3 6 5 4 4 4 3 3 4 5 4 4 3 4 5 3
## [3010] 3 4 3 3 4 4 3 3 3 3 5 5 3 5 4 3 4
## [3027] 4 4 4 3 3 6 3 4 5 4 3 4 4 4 4 3 5
## [3044] 4 7 5 3 6 4 4 5 3 3 4 3 4 3 3 4 3
## [3061] 3 3 4 3 3 4 3 4 3 6 3 10 5 6 3 4 5
## [3078] 4 4 4 5 4 4 3 4 3 4 5 4 3 6 4 3 4
## [3095] 5 3 3 4 4 6 6 6 5 4 3 3 4 4 4 4 4
## [3112] 3 3 5 3 3 5 4 3 3 4 3 5 3 3 3 3 3
## [3129] 4 8 3 4 4 4 6 4 6 6 4 5 4 8 3 5 3
## [3146] 3 3 3 5 3 3 4 4 4 5 8 3 4 4 6 4 7
## [3163] 4 5 5 5 3 3 4 3 4 5 4 3 3 3 6 3 3
## [3180] 5 4 3 4 4 3 4 3 3 4 3 5 5 3 4 3 4
## [3197] 5 3 3 3 3 5 6 3 3 5 4 3 3 3 6 4 5
## [3214] 3 3 3 3 3 4 4 5 3 4 4 4 5 5 3 4 5
## [3231] 5 5 5 4 3 4 4 4 4 4 3 3 3 3 6 4 6
## [3248] 3 6 3 6 4 3 3 4 3 4 3 3 3 4 5 3 7
## [3265] 3 3 3 4 3 3 4 3 3 4 4 3 3 4 5 3 3
## [3282] 4 4 4 3 3 3 5 3 5 3 7 3 4 3 3 3 4
## [3299] 3 4 4 8 3 3 3 4 3 3 3 3 3 3 5 3 3
## [3316] 4 3 5 3 3 3 3 4 3 3 4 4 3 3 3 3 3
## [3333] 3 3 5 4 4 4 5 4 4 3 6 3 5 4 3 3 3
## [3350] 3 7 3 3 3 3 4 3 3 4 3 6 3 3 5 3 5
## [3367] 3 3 4 3 4 4 3 3 3 4 3 3 4 4 3 3 4
## [3384] 4 4 4 3 3 4 4 3 7 3 4 6 3 4 4 5 3
## [3401] 3 4 4 4 5 3 5 3 4 3 4 5 3 3 3 3 3
## [3418] 3 6 4 3 4 3 3 3 4 3 3 3 3 4 5 3 3
## [3435] 4 4 5 3 7 3 4 3 3 3 3 3 6 4 5 6 4
## [3452] 3 3 4 3 4 3 3 4 4 6 3 4 4 4 5 4 4
## [3469] 3 3 6 3 4 4 3 4 3 4 3 5 3 5 4 4 4
## [3486] 3 4 3 3 4 3 5 5 5 4 6 3 5 3 3 5 3
## [3503] 3 3 3 4 3 4 3 5 4 3 4 4 3 3 3 3 4
## [3520] 4 3 4 3 4 6 4 3 4 3 4 3 4 6 4 3 4
## [3537] 4 3 3 5 3 4 3 3 6 3 3 4 3 3 3 3 4
## [3554] 3 5 6 3 3 3 3 3 3 4 5 4 3 4 3 3 4
## [3571] 3 4 4 3 3 4 3 3 3 3 5 4 3 4 4 4 3
## [3588] 4 3 4 4 3 4 3 3 3 3 5 6 3 4 5 3 3
## [3605] 3 6 5 4 5 4 3 4 3 5 3 3 3 3 5 4 4
## [3622] 4 3 3 4 3 4 3 5 4 3 4 3 4 3 3 3 3
## [3639] 4 7 4 3 3 3 4 5 5 3 3 3 3 4 5 5 3
## [3656] 3 3 4 3 4 5 3 3 3 3 4 3 5 3 3 3 4
## [3673] 4 3 3 3 5 4 3 4 3 3 4 3 3 3 3 3 3
## [3690] 6 3 3 3 4 4 3 3 4 3 3 3 3 3 3 3 3
## [3707] 4 3 3 4 4 3 3 4 4 4 3 3 4 3 4 3 3
## [3724] 3 3 5 3 3 3 3 3 3 3 3 4 3 6 3 3 3
## [3741] 3 3 3 5 3 5 3 4 4 3 3 3 4 3 3 3 3
## [3758] 3 3 3 4 4 3 4 4 3 3 3 3 4 3 3 4 3
## [3775] 4 3 5 3 3 4 3 3 4 3 3 4 3 3 3 3 3
## [3792] 5 3 3 6 3 3 4 3 4 3 3 3 4 3 3 4 3
## [3809] 3 3 3 3 3 3 3 3 3 3 3 4 4 5 5 3 3
## [3826] 3 3 3 3 5 3 3 3 3 4 5 3 3 3 3 3 3
## [3843] 5 4 4 5 3 5 4 3 3 6 4 3 4 3 3 3 4
## [3860] 5 3 3 3 3 3 3 5 3 3 4 3 3 3 4 3 3
## [3877] 4 3 3 3 5 3 3 4 3 3 4 4 3 5 4 3 7
## [3894] 5 4 3 4 3 3 4 3 3 4 3 3 3 3 3 3 3
## [3911] 5 3 5 7 3 4 3 4 4 3 4 4 4 3 5 3 3
## [3928] 3 5 3 3 3 3 3 6 4 3 3 3 4 3 3 3 3
## [3945] 3 3 3 3 3 3 4 3 3 3 3 3 4 4 4 3 3
## [3962] 3 3 4 3 3 3 4 3 4 3 3 3 5 4 3 4 3
## [3979] 4 3 3 3 3 3 3 3 4 4 7 3 3 4 3 3 3
## [3996] 4 3 3 3 3 3 4 3 3 3 3 3 3 3 3 4 3
## [4013] 3 4 3 3 3 3 3 5 3 4 4 3 3 3 3 4 3
## [4030] 3 3 5 3 4 4 4 3 3 4 3 4 3 3 3 3 3
## [4047] 3 3 3 3 4 3 4 3 4 3 3 4 3 3 3 3 3
## [4064] 3 4 5 3 3 3 3 3 3 3 3 3 4 3 3 3 3
## [4081] 3 3 3 3 4 3 3 3 3 5 4 4 3 3 3 3 3
## [4098] 3 3 3 3 4 3 3 3 3 4 3 4 3 3 3 4 3
## [4115] 3 3 3 5 4 3 4 3 3 4 3 3 3 4 6 3 3
## [4132] 3 4 4 3 3 4 3 3 3 3 5 3 3 3 3 3 3
## [4149] 4 3 3 4 4 3 4 3 3 3 3 3 3 3 5 3 3
## [4166] 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4 3 4
## [4183] 3 4 4 4 3 4 3 4 3 3 4 6 3 3 3 3 3
## [4200] 3 4 5 3 3 3 3 3 3 4 3 4 3 3 4 4 3
## [4217] 3 4 4 3 3 3 3 3 3 3 4 3 3 3 3 4 3
## [4234] 3 3 4 3 4 3 3 3 3 3 3 3 3 4 3 3 4
## [4251] 3 4 3 4 3 3 3 3 3 3 4 3 3 3 3 4 4
## [4268] 3 3 3 5 4 3 3 3 3 4 3 4 3 3 3 3 3
## [4285] 3 3 3 4 3 3 3 3 3 4 3 3 4 3 3 3 3
## [4302] 3 3 3 3 5 4 3 5 3 5 4 3 4 3 3 4 5
## [4319] 3 4 3 4 4 3 3 3 3 3 4 3 3 3 4 3 3
## [4336] 4 3 4 3 3 3 3 4 3 3 3 3 3 3 4 3 4
## [4353] 3 4 3 3 3 3 4 3 3 3 3 3 3 3 4 3 3
## [4370] 3 3 3 5 4 4 3 4 3 4 4 4 3 3 3 3 3
## [4387] 3 3 3 3 4 3 3 3 3 3 3 4 3 3 3 3 3
## [4404] 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 4
## [4421] 3 3 3 4 3 3 3 3 3 4 3 3 4 3 4 5 3
## [4438] 3 3 3 3 3 3 3 3 3 3 3 4 3 4 3 3 4
## [4455] 3 3 4 3 3 3 3 3 4 3 3 3 3 4 3 3 3
## [4472] 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4489] 3 6 4 3 3 3 3 3 3 3 3 3 3 3 3 4 3
## [4506] 3 3 3 3 3 3 3 3 3 4 3 4 3 4 3 3 3
## [4523] 3 3 3 3 3 3 3 3 3 3 3 4 4 3 3 3 3
## [4540] 3 3 3 3 3 3 3 3 3 3 3 5 3 3 4 3 3
## [4557] 3 3 3 4 3 4 3 3 3 3 3 3 3 3 4 3 3
## [4574] 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3
## [4591] 3 3 3 3 3 3 4 3 3 3 3 4 3 3 3 3 3
## [4608] 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 4
## [4625] 3 3 4 3 3 4 3 3 3 3 3 3 3 3 3 3 3
## [4642] 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3
## [4659] 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3
## [4676] 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4693] 3 3 3 3 3 3 4 3 3 3 3 3 4 3 3 3 3
## [4710] 3 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3
## [4727] 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 3
## [4744] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4761] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4778] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4795] 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 4 3
## [4812] 3 3 4 3 4 3 3 3 3 3 3 3 3 3 3 4 3
## [4829] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3
## [4846] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3
## [4863] 3 3 3 3 3 3 4 3 3 3 3 3 3 3 3 3 4
## [4880] 3 3 3 3 3 3 3 3 3 4 3 3 3 3 3 3 4
## [4897] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4914] 3 3 4 3 3 4 3 3 3 3 3 3 3 3 3 3 3
## [4931] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4948] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4965] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4982] 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
## [4999] 3 3 3 3 3 3Find and plot the degree distribution in i) linear scale
plot((degree.distribution(g5004,cumulative = FALSE,loops=FALSE,normalized=FALSE,mode=c("total"))),main = "Degree Distribution for 5004 Nodes",xlab = "Degrees",ylab = "Fractions")
and ii) log-log scale.
plot((degree.distribution(g5004,cumulative = FALSE,loops=FALSE,normalized=FALSE,mode=c("total"))),main = "Degree Distribution for 5004 Nodes Log/Log",xlab = "Degrees",ylab = "Fractions",log = "xy")
1(b): Repeat 1(a) but instead of always adding 3 links for each new node, add either 1, 2, or 3 links with equal probability. That is, the new node links to 1 node with probability 1/3, links to 2 nodes with probability 1/3, and to 3 nodes with probability 1/3. How many links does the final network have? Plot the degree distribution using i) linear scale and ii) log-log scale. 1(a): Create a network with 4 nodes that are connected to each other i.e., a complete graph with 4 nodes and the degree for all is 3.
n<-4
p.<-1
g<-erdos.renyi.game(n,p.,type = c("gnp"),directed = FALSE,loops = FALSE)
plot.igraph(g)
g## IGRAPH 1bc296e U--- 4 6 -- Erdos renyi (gnp) graph
## + attr: name (g/c), type (g/c), loops (g/l), p (g/n)
## + edges from 1bc296e:
## [1] 1--2 1--3 1--4 2--3 2--4 3--4Number of nodes is 4 Number of links is 6
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g,v=V(g), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 3 3 3 3Adding a new node (the 5th one) to this existing network.
v<-c(0,.333,.333,.333)
g5<-barabasi.game(5, power = 1, m = NULL, out.dist = v, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g)
plot.igraph(g5)
g5## IGRAPH 1bdd5be U--- 5 7 -- Barabasi graph
## + attr: name (g/c), power (g/n), m (g/x), zero.appeal (g/n),
## | algorithm (g/c)
## + edges from 1bdd5be:
## [1] 1--2 1--3 1--4 2--3 2--4 3--4 2--5Number of nodes is 5 Number of links is 7
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g5,v=V(g5), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 3 4 3 3 1Add the 6th node in a similar fashion.
g6<-barabasi.game(6, power = 1, m = NULL, out.dist = v, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g5)
plot.igraph(g6)
g6## IGRAPH 1bf75e2 U--- 6 10 -- Barabasi graph
## + attr: name (g/c), power (g/n), m (g/x), zero.appeal (g/n),
## | algorithm (g/c)
## + edges from 1bf75e2:
## [1] 1--2 1--3 1--4 2--3 2--4 3--4 2--5 3--6 2--6 5--6Number of nodes is 6 Number of links is 8
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g6,v=V(g6), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 3 5 4 3 2 3Continue to add 5000 nodes.
In the following graph, larger Nodes have a higher degree and are shown in the center. You can also notice nodes with single links on the outskirts of the graph since we are adding a choice of links of 1,2, or 3 when a node enters.
g5004<-barabasi.game(5004, power = 1, m = NULL, out.dist = v, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g6)
deg <- degree(g5004, mode="all")
l <- layout_with_fr(g5004)
l <- norm_coords(l, ymin=-15.3, ymax=15.3, xmin=-23, xmax=23)
par(mfrow=c(1,1), mar=c(0,0,0,0))
plot(g5004, rescale=F, layout=l*.07,vertex.label=NA,vertex.size=deg*.1,edge.width=.0000000000000000001,edge.curved=.1)
g5004## IGRAPH 1c109cb U--- 5004 10042 -- Barabasi graph
## + attr: name (g/c), power (g/n), m (g/x), zero.appeal (g/n),
## | algorithm (g/c)
## + edges from 1c109cb:
## [1] 1-- 2 1-- 3 1-- 4 2-- 3 2-- 4 3-- 4 2-- 5 3-- 6 2-- 6 5-- 6
## [11] 5-- 7 4-- 7 1-- 8 5-- 8 4-- 9 7--10 1--10 4--11 7--12 2--13
## [21] 5--13 7--14 3--14 2--15 3--16 2--16 10--16 12--17 8--18 11--18
## [31] 5--19 2--19 11--19 5--20 2--20 3--20 20--21 3--21 14--21 6--22
## [41] 15--22 3--23 21--23 6--24 23--25 20--25 1--26 2--26 2--27 20--28
## [51] 16--28 4--29 5--29 21--29 2--30 21--30 10--30 12--31 3--31 5--31
## [61] 5--32 3--33 32--33 26--34 13--34 31--34 10--35 2--35 12--35 3--36
## + ... omitted several edgesNumber of nodes is 5004 Number of links is 9993
Degree for each node in order(Node 1 ..2..3…4..n) below:
degree(g5004,v=V(g5004), mode = c("total"),loops = FALSE, normalized = FALSE)## [1] 29 108 71 72 75 52 29 7 7 41 34 31 20 14 4 18 8
## [18] 35 31 53 50 21 27 47 18 16 22 32 41 28 32 30 42 7
## [35] 25 36 21 19 12 39 2 29 16 24 4 22 20 20 28 22 17
## [52] 13 31 11 14 5 35 27 6 20 7 16 6 35 6 14 10 2
## [69] 22 14 10 11 5 30 33 9 22 30 16 45 10 10 20 9 36
## [86] 21 9 23 17 6 13 5 4 31 25 6 4 12 6 9 14 22
## [103] 32 26 8 18 17 11 15 7 3 9 26 13 17 10 10 6 2
## [120] 14 14 21 10 13 6 3 8 1 9 13 8 9 7 3 7 7
## [137] 5 6 16 9 12 13 18 10 16 28 10 2 6 17 16 7 6
## [154] 9 19 5 7 11 7 7 13 7 9 8 5 11 9 5 13 4
## [171] 4 2 13 12 4 15 17 45 19 10 10 11 8 6 23 4 4
## [188] 13 12 11 7 19 11 17 4 3 6 9 18 18 19 21 10 5
## [205] 13 8 11 11 4 8 2 7 4 5 4 7 7 16 10 14 11
## [222] 6 3 8 11 6 7 1 6 15 6 9 10 12 21 12 9 8
## [239] 9 17 8 2 10 12 10 6 13 7 6 13 13 9 17 6 2
## [256] 11 19 10 5 8 11 8 6 15 16 5 13 15 8 8 7 18
## [273] 10 12 10 5 10 1 8 14 9 10 6 11 6 4 13 13 13
## [290] 9 9 13 16 1 7 3 14 9 9 9 8 12 8 5 6 3
## [307] 3 11 4 3 1 1 6 7 17 5 6 5 5 15 2 2 14
## [324] 9 4 6 7 10 11 2 4 9 8 6 6 10 4 14 5 2
## [341] 5 4 17 4 21 6 9 8 4 6 22 4 6 11 12 18 15
## [358] 7 2 8 22 8 8 6 2 11 16 5 15 5 11 3 3 11
## [375] 3 4 5 11 2 2 5 8 3 4 6 11 5 5 8 14 1
## [392] 5 5 10 8 4 10 14 11 4 14 2 4 4 4 5 15 11
## [409] 13 14 11 3 8 4 2 10 7 2 1 11 3 11 10 10 7
## [426] 13 6 3 2 9 4 3 11 6 15 4 9 8 6 12 10 7
## [443] 12 12 6 6 9 10 7 6 6 1 9 3 3 2 5 4 9
## [460] 11 2 1 9 3 7 16 2 3 2 11 4 10 9 9 6 6
## [477] 8 6 9 5 2 2 7 5 3 2 14 17 4 2 5 1 8
## [494] 11 14 9 5 7 2 1 7 8 7 22 5 2 2 5 9 5
## [511] 7 17 2 9 2 8 4 9 1 3 1 6 4 5 9 6 6
## [528] 8 9 10 21 10 7 2 4 14 6 4 4 11 8 9 12 3
## [545] 3 2 5 6 10 9 5 5 6 3 8 2 9 4 3 5 10
## [562] 3 8 10 1 7 8 4 6 3 3 6 1 4 6 6 8 5
## [579] 1 2 4 12 9 1 11 5 2 9 3 15 4 1 2 3 7
## [596] 10 2 5 7 5 8 5 5 5 1 6 9 7 4 5 5 3
## [613] 6 1 3 9 6 2 2 6 10 4 8 7 8 4 10 7 12
## [630] 8 10 6 3 5 2 13 13 10 8 4 7 2 5 7 5 4
## [647] 3 5 6 5 1 7 10 8 3 13 1 19 6 3 8 3 13
## [664] 5 4 6 4 1 9 10 3 5 11 6 5 2 7 3 3 9
## [681] 6 6 8 16 2 8 8 10 6 3 7 1 8 9 7 21 7
## [698] 4 8 4 2 5 1 5 8 8 2 9 2 8 2 5 1 9
## [715] 3 4 5 6 6 2 3 6 5 6 11 4 2 8 8 2 6
## [732] 9 4 1 2 8 6 11 10 2 7 4 2 4 6 3 8 4
## [749] 6 2 8 11 4 4 3 6 7 8 1 12 7 2 3 2 2
## [766] 8 1 4 4 6 6 2 6 6 5 2 6 5 2 7 7 6
## [783] 3 10 6 7 4 3 3 6 4 10 11 4 1 10 8 7 8
## [800] 6 2 4 2 12 1 4 9 2 5 3 6 9 4 3 6 4
## [817] 1 7 1 6 2 7 14 7 7 7 2 7 5 3 6 3 10
## [834] 3 4 3 8 4 10 3 5 4 4 3 12 2 2 4 7 5
## [851] 6 5 3 1 5 7 7 11 3 13 4 8 7 4 5 4 4
## [868] 6 8 3 2 2 6 2 11 4 5 2 2 4 1 4 6 6
## [885] 5 1 8 7 5 3 6 5 3 12 2 5 3 3 2 7 7
## [902] 1 3 12 8 2 4 1 8 5 12 4 7 5 12 1 8 6
## [919] 4 3 2 5 1 1 3 10 7 1 9 4 5 3 5 6 5
## [936] 5 3 3 6 6 8 9 3 1 9 5 3 2 5 3 4 2
## [953] 1 4 9 5 2 11 2 9 4 9 3 9 3 2 5 3 8
## [970] 7 5 6 2 9 1 1 5 7 1 5 10 3 2 3 9 19
## [987] 1 4 2 8 1 3 1 4 8 6 8 3 4 6 4 4 5
## [1004] 4 2 6 3 5 2 5 3 4 1 2 3 3 3 6 5 2
## [1021] 4 5 2 5 4 8 2 7 1 3 5 5 2 5 6 2 2
## [1038] 2 1 1 5 5 2 5 5 10 2 4 3 4 4 3 4 3
## [1055] 2 1 2 5 8 4 2 8 8 4 3 1 2 2 5 4 2
## [1072] 3 2 3 2 3 3 3 9 3 6 6 1 4 4 4 11 1
## [1089] 8 6 9 3 3 4 6 2 4 7 3 7 2 5 1 3 3
## [1106] 4 1 2 9 3 7 3 8 4 7 3 3 8 10 4 1 2
## [1123] 3 4 12 4 2 5 4 4 5 4 3 5 5 4 8 3 9
## [1140] 4 3 12 3 6 6 2 3 6 7 4 4 4 5 1 3 2
## [1157] 1 1 1 3 3 8 3 5 10 3 1 10 5 4 2 4 8
## [1174] 12 1 4 3 3 1 5 6 5 5 5 7 4 1 4 7 2
## [1191] 3 4 5 5 3 4 2 3 2 4 4 8 8 4 5 4 6
## [1208] 1 8 7 2 4 3 2 3 13 7 3 6 5 4 4 4 1
## [1225] 2 11 3 2 3 1 4 1 5 6 10 7 4 6 4 4 1
## [1242] 3 1 10 7 3 3 6 4 5 2 8 5 1 5 2 8 7
## [1259] 4 1 3 3 6 6 5 2 8 4 6 2 2 2 1 3 1
## [1276] 7 8 3 5 5 5 3 2 3 2 2 4 4 6 4 5 3
## [1293] 3 2 9 5 1 4 1 4 11 5 11 1 6 2 3 7 8
## [1310] 1 1 7 3 8 1 6 9 5 1 3 11 2 4 6 5 4
## [1327] 6 3 3 1 3 2 4 8 1 3 9 2 2 3 2 1 6
## [1344] 4 4 4 2 5 3 4 5 6 4 2 3 2 8 5 5 3
## [1361] 8 1 4 7 3 2 2 4 8 3 2 4 6 4 2 4 1
## [1378] 3 5 5 4 2 2 2 7 2 4 2 4 2 5 3 3 5
## [1395] 2 3 6 3 6 2 1 2 6 5 1 2 3 3 6 7 4
## [1412] 6 4 4 6 7 10 2 1 2 2 1 3 3 5 2 7 7
## [1429] 2 5 3 3 12 1 6 1 2 5 7 10 4 2 5 2 3
## [1446] 3 10 5 5 1 2 3 3 2 2 1 2 1 2 5 3 4
## [1463] 4 2 2 2 5 1 2 2 2 2 3 2 2 1 5 3 2
## [1480] 1 6 5 3 2 2 1 6 5 1 2 3 2 3 1 5 6
## [1497] 5 1 1 4 12 4 3 3 8 5 2 6 4 9 5 4 5
## [1514] 1 7 2 2 4 3 4 3 2 3 1 2 3 1 3 3 2
## [1531] 3 5 1 7 4 3 7 4 2 1 1 4 5 3 5 2 4
## [1548] 1 6 5 4 4 2 4 3 1 1 4 1 1 6 8 5 5
## [1565] 1 4 6 4 3 6 7 4 5 2 10 1 4 6 4 3 4
## [1582] 5 6 5 3 3 1 9 6 3 2 1 8 2 4 5 3 8
## [1599] 5 4 1 3 6 4 6 3 3 3 2 3 5 4 3 1 3
## [1616] 2 1 5 1 6 4 7 10 3 5 7 3 3 2 8 2 6
## [1633] 3 6 2 3 4 4 5 3 4 5 2 3 2 6 3 1 3
## [1650] 5 5 11 5 2 2 1 4 2 6 3 4 3 1 4 4 3
## [1667] 3 4 2 2 3 1 1 2 4 2 3 4 3 4 4 3 3
## [1684] 1 3 8 5 4 6 4 4 4 3 5 2 2 1 8 4 5
## [1701] 4 5 3 3 7 4 1 1 2 7 5 2 2 3 8 1 2
## [1718] 8 4 7 4 3 11 1 2 5 3 4 4 4 2 3 6 4
## [1735] 1 4 4 4 3 4 5 4 2 3 5 2 4 6 4 1 7
## [1752] 4 2 7 6 1 1 6 3 4 4 6 4 4 2 1 6 3
## [1769] 4 6 4 3 8 5 4 1 5 2 2 6 1 1 1 5 1
## [1786] 5 1 3 4 4 1 3 5 3 8 5 3 4 1 2 5 6
## [1803] 2 4 8 3 2 3 3 1 1 2 4 3 4 1 10 3 4
## [1820] 4 2 6 7 3 1 6 3 4 2 3 5 3 4 1 4 2
## [1837] 7 5 3 1 5 6 2 4 4 5 2 2 9 6 5 3 5
## [1854] 3 5 1 2 3 1 1 3 4 2 5 7 4 2 1 4 2
## [1871] 3 3 2 3 4 1 3 5 3 6 5 1 4 5 3 3 3
## [1888] 5 3 4 3 4 3 3 2 5 7 3 3 2 3 2 2 5
## [1905] 3 5 5 3 1 5 3 6 3 5 3 6 4 3 2 1 3
## [1922] 2 2 3 6 5 4 2 8 2 5 1 4 3 3 6 6 2
## [1939] 2 4 2 5 4 7 3 2 2 5 1 5 1 5 3 3 5
## [1956] 5 3 3 4 4 1 3 3 1 1 3 3 4 10 3 3 4
## [1973] 1 2 1 2 3 2 1 1 6 3 2 6 4 5 3 3 6
## [1990] 4 6 2 3 2 8 1 1 2 1 4 1 1 5 7 2 2
## [2007] 6 3 4 1 1 2 4 1 4 6 4 3 2 5 2 4 4
## [2024] 5 3 3 2 5 3 2 4 3 2 3 7 4 1 4 4 3
## [2041] 6 2 4 2 4 2 3 4 2 2 2 1 4 2 4 2 10
## [2058] 2 2 3 3 6 5 1 2 5 6 7 4 4 1 3 1 4
## [2075] 6 2 4 1 2 4 4 1 4 3 2 3 3 4 3 2 3
## [2092] 2 3 5 3 3 1 4 3 3 6 2 1 2 2 2 3 12
## [2109] 3 4 2 1 2 1 3 2 3 4 7 1 4 3 2 3 5
## [2126] 4 2 3 4 4 1 3 1 3 1 5 3 2 4 6 2 2
## [2143] 2 9 1 2 6 1 1 2 3 4 5 2 3 1 2 2 3
## [2160] 2 2 2 4 5 5 3 3 1 4 3 2 1 4 5 2 4
## [2177] 4 4 4 7 1 1 5 3 2 8 2 5 5 3 2 4 1
## [2194] 1 3 4 5 5 1 2 1 1 3 6 2 3 2 3 1 1
## [2211] 4 2 1 2 4 1 5 3 6 1 3 1 1 3 3 4 2
## [2228] 3 3 5 3 4 3 4 4 3 2 1 2 1 6 2 4 2
## [2245] 4 2 1 4 4 5 1 5 3 2 3 2 5 3 4 7 4
## [2262] 4 3 3 2 2 5 4 3 3 3 2 5 2 3 2 1 4
## [2279] 3 7 6 5 1 2 4 5 3 4 2 2 8 3 1 6 6
## [2296] 3 7 2 2 1 3 4 2 2 3 5 4 4 2 4 3 2
## [2313] 2 7 1 3 5 3 2 4 2 2 1 1 2 1 4 3 1
## [2330] 2 4 1 3 2 3 3 6 5 6 3 1 3 7 3 1 2
## [2347] 4 6 4 5 2 1 1 2 4 2 3 5 4 3 2 2 4
## [2364] 3 2 4 1 3 2 7 4 4 3 1 2 5 1 2 1 3
## [2381] 1 2 2 4 2 1 2 2 4 3 3 2 4 3 3 5 2
## [2398] 1 1 2 4 3 5 3 1 3 5 3 4 6 2 4 4 2
## [2415] 3 1 1 3 7 1 3 2 3 4 1 4 4 3 2 2 3
## [2432] 3 2 2 2 3 4 1 3 5 2 2 2 3 5 2 5 5
## [2449] 3 3 3 3 1 4 2 1 2 1 4 4 3 4 2 2 2
## [2466] 2 4 3 5 1 5 3 5 3 1 3 2 2 8 1 1 3
## [2483] 2 2 4 6 2 3 4 4 3 3 1 4 3 5 5 3 2
## [2500] 4 3 2 3 3 2 1 3 6 2 4 2 4 3 5 3 4
## [2517] 3 3 4 2 9 3 2 2 3 2 5 2 3 2 5 4 4
## [2534] 1 2 3 2 1 3 1 1 1 4 2 1 2 5 5 2 4
## [2551] 2 6 4 2 4 2 3 2 4 4 3 6 4 3 2 1 3
## [2568] 3 1 2 4 4 3 2 2 5 4 2 7 3 6 4 1 6
## [2585] 2 7 2 3 2 4 2 2 2 5 4 8 1 1 2 5 4
## [2602] 2 1 1 1 5 10 3 1 3 3 3 4 1 4 3 3 4
## [2619] 5 1 3 2 1 3 4 2 3 4 4 4 3 2 6 2 2
## [2636] 2 3 3 2 5 4 3 3 3 3 6 1 3 2 4 4 4
## [2653] 3 1 5 3 1 5 3 2 4 6 4 4 3 1 3 2 4
## [2670] 4 5 3 3 2 3 2 3 4 5 1 3 1 4 3 3 4
## [2687] 5 2 5 1 4 3 4 2 5 1 2 4 3 4 3 2 4
## [2704] 8 2 4 1 3 4 2 4 4 4 4 1 1 4 5 6 4
## [2721] 3 2 3 2 2 4 3 5 3 4 1 1 2 2 3 1 1
## [2738] 7 2 1 1 2 4 3 1 3 2 4 1 2 1 3 3 1
## [2755] 1 2 2 4 7 7 2 2 2 5 3 3 1 2 4 4 2
## [2772] 8 5 3 4 3 5 3 6 4 3 2 1 1 3 4 1 1
## [2789] 4 2 3 4 3 1 3 2 1 3 1 2 4 1 2 4 2
## [2806] 1 3 2 1 4 2 6 3 1 1 1 1 4 3 4 1 3
## [2823] 3 3 3 2 3 3 2 5 3 5 1 1 2 1 3 4 4
## [2840] 2 1 2 3 2 2 2 1 1 1 3 4 2 4 4 2 2
## [2857] 2 3 4 4 1 4 4 1 1 3 3 1 4 2 5 3 1
## [2874] 3 1 2 1 3 1 4 2 2 2 4 5 3 3 2 4 1
## [2891] 4 9 1 2 6 2 2 3 1 8 2 2 4 2 3 1 4
## [2908] 2 6 4 1 4 3 4 2 3 3 2 2 1 2 1 4 5
## [2925] 3 2 2 5 2 1 1 5 4 3 1 2 1 2 5 3 2
## [2942] 2 5 5 1 3 2 4 3 2 2 4 2 6 4 3 1 2
## [2959] 1 5 2 5 4 1 5 1 5 3 3 3 3 1 3 1 3
## [2976] 3 2 2 1 1 3 3 2 2 3 6 3 6 1 4 4 4
## [2993] 2 2 5 2 2 3 6 1 2 5 3 2 3 1 2 2 1
## [3010] 4 4 3 1 5 2 4 4 2 2 3 1 1 2 3 3 4
## [3027] 2 3 1 2 2 2 2 2 3 1 4 6 2 1 5 1 1
## [3044] 1 2 4 4 1 3 4 4 3 1 4 5 1 4 3 1 1
## [3061] 3 4 1 5 3 4 3 1 2 1 1 3 2 4 2 3 2
## [3078] 2 3 3 3 5 4 3 5 2 1 1 1 2 4 3 1 2
## [3095] 2 5 3 3 2 2 1 2 1 1 3 2 3 1 3 4 4
## [3112] 2 3 1 2 4 3 1 4 1 3 3 5 3 2 6 1 3
## [3129] 3 3 3 1 3 3 2 5 1 1 3 1 1 2 2 1 1
## [3146] 5 5 1 1 2 7 2 3 1 3 2 2 2 3 3 2 3
## [3163] 3 3 1 4 1 1 2 3 1 4 3 3 4 3 2 3 1
## [3180] 6 1 3 2 1 2 3 4 1 2 3 4 1 2 2 3 3
## [3197] 4 3 2 1 2 4 1 1 3 4 2 3 2 3 4 4 4
## [3214] 2 1 4 2 3 1 2 3 3 4 5 1 2 3 2 3 2
## [3231] 4 2 3 2 3 3 2 1 3 3 3 2 3 4 1 2 3
## [3248] 3 3 3 1 3 1 4 3 3 2 3 1 5 2 1 2 2
## [3265] 4 6 1 1 4 2 6 5 3 3 3 2 3 1 4 1 1
## [3282] 2 3 2 3 1 3 3 2 1 3 1 3 4 2 5 2 3
## [3299] 2 3 2 3 4 1 1 4 3 5 1 3 3 4 1 3 4
## [3316] 2 1 1 3 1 7 1 2 4 1 2 2 1 1 3 4 4
## [3333] 2 3 1 3 2 1 3 1 2 1 1 1 4 3 3 1 2
## [3350] 1 4 3 2 2 3 3 2 4 4 2 5 3 1 1 2 1
## [3367] 3 3 3 1 2 3 4 6 3 4 2 1 1 1 2 5 1
## [3384] 2 5 3 2 3 3 1 1 5 3 2 4 3 1 3 2 2
## [3401] 2 2 3 2 4 1 2 4 3 3 7 2 1 2 3 2 2
## [3418] 3 3 2 1 2 4 2 3 4 2 3 2 1 1 2 2 4
## [3435] 2 4 1 1 2 3 2 6 2 3 1 3 4 3 4 1 3
## [3452] 3 3 4 2 5 3 2 4 3 2 1 2 2 2 3 1 3
## [3469] 5 3 1 2 1 2 1 1 1 2 3 3 5 1 3 1 2
## [3486] 3 3 3 1 4 1 2 3 1 2 2 3 5 2 2 1 3
## [3503] 5 2 1 3 2 1 1 1 2 3 1 3 2 3 1 3 3
## [3520] 1 2 4 3 1 4 2 2 2 3 2 1 4 2 4 1 2
## [3537] 2 5 1 2 3 1 4 3 2 1 4 2 3 2 1 3 3
## [3554] 3 1 3 2 3 2 4 3 1 4 2 1 2 3 4 3 2
## [3571] 1 5 1 2 3 1 2 2 3 2 2 1 1 3 1 2 3
## [3588] 3 1 3 4 3 2 1 1 3 3 2 3 3 7 3 5 1
## [3605] 1 4 1 3 1 2 3 2 2 4 5 3 2 2 1 3 5
## [3622] 3 3 3 4 3 1 1 4 3 1 3 1 1 2 3 3 4
## [3639] 3 3 1 1 2 1 2 1 4 2 3 3 3 2 3 1 4
## [3656] 4 2 2 3 3 4 3 3 2 3 3 1 1 4 2 1 3
## [3673] 1 1 2 3 3 3 1 3 2 2 3 2 3 3 4 3 4
## [3690] 1 2 2 2 2 2 3 2 1 1 4 1 3 3 2 2 1
## [3707] 3 1 3 3 3 1 4 3 2 3 1 3 3 2 3 4 3
## [3724] 3 3 2 2 3 2 2 3 3 3 2 2 1 3 3 1 2
## [3741] 3 3 1 3 2 2 1 4 5 3 1 4 2 3 3 1 4
## [3758] 2 1 3 4 3 2 1 2 2 1 1 1 2 3 3 4 1
## [3775] 2 3 3 3 1 2 2 3 2 2 2 2 1 2 3 4 4
## [3792] 4 2 2 3 3 1 1 3 4 2 2 2 4 1 3 2 1
## [3809] 1 1 2 1 1 2 2 1 4 3 2 1 2 3 4 3 1
## [3826] 2 1 4 3 1 3 2 1 4 2 2 1 1 3 3 1 1
## [3843] 4 3 2 1 2 2 2 3 1 2 3 4 1 3 3 2 3
## [3860] 3 2 3 3 4 2 1 1 1 4 2 2 2 2 3 3 1
## [3877] 1 2 2 2 2 2 2 1 2 3 2 1 4 1 1 1 2
## [3894] 3 3 3 2 2 1 3 3 1 1 1 4 2 4 4 1 3
## [3911] 2 3 1 3 1 3 5 4 3 2 2 1 5 3 1 3 2
## [3928] 2 3 3 4 2 3 1 2 1 2 1 4 3 3 1 3 4
## [3945] 2 2 1 2 3 4 3 2 2 3 2 4 3 5 3 2 1
## [3962] 2 2 3 3 1 3 1 2 1 3 3 3 2 1 2 1 4
## [3979] 1 1 2 1 3 1 1 3 2 4 2 3 3 3 1 1 1
## [3996] 3 3 5 2 2 2 1 4 3 2 1 2 3 2 2 2 6
## [4013] 1 1 3 1 3 2 3 1 3 3 1 3 3 1 4 2 1
## [4030] 2 5 3 4 1 2 2 1 4 2 2 3 1 4 4 3 1
## [4047] 1 3 2 4 1 4 3 2 3 3 1 3 1 2 1 2 1
## [4064] 3 5 1 2 4 3 2 1 2 2 3 2 2 3 1 3 2
## [4081] 4 3 3 1 3 3 1 3 1 3 3 3 3 3 5 1 3
## [4098] 3 1 2 1 3 3 1 5 2 1 1 3 3 2 3 6 2
## [4115] 1 3 2 2 1 3 1 4 4 3 4 2 1 2 2 4 1
## [4132] 4 2 4 3 3 2 3 3 2 3 1 2 1 3 3 3 1
## [4149] 3 3 2 2 1 1 1 2 2 3 2 2 4 2 3 1 1
## [4166] 2 1 2 3 3 3 3 2 3 3 2 3 1 2 4 1 2
## [4183] 3 3 2 4 1 2 4 2 3 3 2 1 3 3 2 3 1
## [4200] 4 3 4 3 1 1 4 5 3 4 2 1 4 2 3 1 3
## [4217] 2 3 3 2 2 2 4 1 2 2 3 3 2 3 2 1 2
## [4234] 3 3 2 3 1 2 4 3 1 2 1 4 2 3 1 3 1
## [4251] 3 1 3 3 3 1 2 3 2 1 2 2 3 3 1 4 2
## [4268] 2 1 1 2 2 2 2 2 1 1 3 1 1 2 3 2 3
## [4285] 2 3 1 3 3 2 3 1 2 5 2 2 1 3 1 3 1
## [4302] 2 2 2 1 3 1 4 1 2 3 1 3 2 4 3 2 2
## [4319] 3 1 1 2 4 3 1 3 3 2 2 3 3 1 3 3 3
## [4336] 1 1 1 3 2 1 1 1 2 1 2 3 2 1 1 4 1
## [4353] 2 3 1 3 1 2 3 2 1 1 2 2 4 2 3 3 2
## [4370] 3 1 2 4 1 1 1 1 1 3 2 4 1 3 1 2 2
## [4387] 1 1 3 1 3 1 1 2 3 2 2 2 1 3 1 3 3
## [4404] 5 2 3 1 4 4 1 2 1 3 4 1 3 2 2 3 1
## [4421] 1 3 2 3 3 1 1 2 1 2 1 1 1 2 1 1 2
## [4438] 1 3 2 4 3 6 2 2 1 1 2 2 1 3 3 1 1
## [4455] 1 2 2 2 4 3 2 4 3 2 2 2 2 2 3 4 1
## [4472] 2 2 2 3 2 3 3 1 1 2 3 1 1 3 4 1 2
## [4489] 2 3 3 2 3 1 4 2 3 3 3 3 2 1 3 1 1
## [4506] 3 1 3 3 3 3 2 3 3 1 1 3 2 3 4 3 3
## [4523] 3 2 2 2 1 1 2 3 2 2 3 2 2 2 2 4 1
## [4540] 4 3 2 3 4 1 3 3 4 1 3 1 3 2 2 2 1
## [4557] 1 1 1 3 4 2 2 1 1 2 2 4 1 1 4 3 2
## [4574] 2 3 2 2 1 4 2 3 1 1 2 3 3 1 3 3 1
## [4591] 1 3 1 2 2 1 3 4 1 4 2 1 2 3 2 3 3
## [4608] 3 4 2 2 3 3 3 3 3 1 1 2 2 2 3 2 1
## [4625] 2 2 2 2 1 3 3 2 1 3 2 3 2 2 1 3 2
## [4642] 3 3 3 2 3 3 3 3 3 3 1 2 2 3 2 3 2
## [4659] 1 2 3 3 3 1 3 2 2 2 2 2 3 1 5 2 3
## [4676] 1 1 2 3 3 1 1 3 3 3 2 3 2 3 2 2 1
## [4693] 3 2 3 1 2 1 2 3 2 2 1 3 3 1 3 1 2
## [4710] 3 1 1 2 1 3 3 2 2 2 3 3 2 1 2 3 3
## [4727] 2 1 1 2 3 1 2 1 3 1 3 2 1 4 3 1 2
## [4744] 3 1 2 3 1 2 3 4 1 2 2 2 2 2 2 3 2
## [4761] 1 3 2 3 2 3 1 1 1 3 3 1 3 3 2 3 1
## [4778] 3 2 1 1 1 4 3 2 3 1 1 3 2 2 2 3 4
## [4795] 1 1 1 3 1 3 1 3 2 3 1 2 3 4 3 1 1
## [4812] 2 2 1 1 3 2 2 2 2 1 1 3 3 1 3 3 2
## [4829] 2 2 3 2 3 3 3 2 1 2 1 3 1 3 2 1 3
## [4846] 1 3 1 2 2 2 3 2 3 2 1 3 3 1 1 3 1
## [4863] 3 1 1 3 3 1 3 1 2 3 1 2 3 2 3 1 2
## [4880] 3 2 3 1 1 2 1 2 3 2 1 2 1 1 1 1 2
## [4897] 1 2 1 1 3 3 1 3 1 1 2 3 2 1 3 1 3
## [4914] 1 2 1 2 2 2 1 2 1 2 1 2 1 2 1 3 2
## [4931] 3 3 2 1 1 1 3 3 3 3 3 3 3 2 2 1 1
## [4948] 2 3 1 3 2 3 1 3 2 1 2 3 2 3 3 3 2
## [4965] 2 2 3 1 3 3 1 3 1 3 2 1 1 2 2 1 2
## [4982] 3 1 1 3 1 1 2 3 2 1 2 3 3 3 3 1 1
## [4999] 2 1 3 1 3 2Find and plot the degree distribution in i) linear scale
plot((degree.distribution(g5004,cumulative = FALSE,loops=FALSE,normalized=FALSE,mode=c("total"))),main = "Degree Distribution for 5004 Nodes",xlab = "Degrees",ylab = "Fractions")
and ii) log-log scale.
plot((degree.distribution(g5004,cumulative = FALSE,loops=FALSE,normalized=FALSE,mode=c("total"))),main = "Degree Distribution for 5004 Nodes Log/Log",xlab = "Degrees",ylab = "Fractions",log = "xy")
- (4 points) Find the degree distribution of the Barabasi-Albert model analytically. That is, each time a new node arrives and connects with m nodes proportional to the existing nodes’ degree (which is nothing but the preferential attachment model). Hint: Refer to the book.
EXtra Credit Assignment Part 2 (The 2, 5004 node newtworks are already plotted in their corresponding sections) Following are the 2 network plots for 100 additional nodes. 3 Fixed links when arriving into network: In the following graph, larger Nodes have a higher degree and are shown in the center.
g5004<-barabasi.game(104, power = 1, m = 3, out.dist = NULL, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g)
deg <- degree(g5004, mode="all")
l <- layout_with_fr(g5004)
l <- norm_coords(l, ymin=-15.3, ymax=15.3, xmin=-23, xmax=23)
par(mfrow=c(1,1), mar=c(0,0,0,0))
plot(g5004, rescale=F, layout=l*.07,vertex.label=NA,vertex.size=deg*.1,edge.width=.0000000000000000001,edge.curved=.1)
Choice of 1,2, or 3 links: In the following graph, larger Nodes have a higher degree and are shown in the center. You can also notice nodes with single links on the outskirts of the graph since we are adding a choice of links of 1,2, or 3 when a node enters.
g5004<-barabasi.game(104, power = 1, m = NULL, out.dist = v, out.seq = NULL,
out.pref = FALSE, zero.appeal = 1, directed = FALSE,
algorithm = c("psumtree"), start.graph = g)
deg <- degree(g5004, mode="all")
l <- layout_with_fr(g5004)
l <- norm_coords(l, ymin=-15.3, ymax=15.3, xmin=-23, xmax=23)
par(mfrow=c(1,1), mar=c(0,0,0,0))
plot(g5004, rescale=F, layout=l*.07,vertex.label=NA,vertex.size=deg*.1,edge.width=.0000000000000000001,edge.curved=.1)