Visualization of an undirected social network of frequent associations between 62 dolphins in a community living off Doubtful Sound, New Zealand, as compiled by Lusseau et al. (2003).

REFERENCES :

D. Lusseau, K. Schneider, O. J. Boisseau, P. Haase, E. Slooten, and S. M. Dawson, The bottlenose dolphin community of Doubtful Sound features a large proportion of long-lasting associations, Behavioral Ecology and Sociobiology 54, 396-405 (2003).

https://networkdata.ics.uci.edu/data.php?id=6

VISUALIZATION :

  1. What is the data that you chose? Why? : We selected the above dataset on the UCI repository as we were interested in the communities and interactions among dolphins.

  2. Did you use a subset of the data? If so, what was it? : The full gml file was used. GML (Graph Modeling Language) is a text file format supporting network data with a very easy syntax.

library(igraph)
## Warning: package 'igraph' was built under R version 3.2.1
## 
## Attaching package: 'igraph'
## 
## The following objects are masked from 'package:stats':
## 
##     decompose, spectrum
## 
## The following object is masked from 'package:base':
## 
##     union
g<-read.graph("dolphins.gml",format=c("gml"))
g
## IGRAPH U--- 62 159 -- 
## + attr: id (v/n), label (v/c)
## + edges:
##  [1]  4-- 9  6--10  7--10  1--11  3--11  6--14  7--14 10--14  1--15  4--15
## [11]  1--16 15--17  2--18  7--18 10--18 14--18 16--19  2--20  8--20  9--21
## [21] 17--21 19--21 19--22 18--23 15--25 16--25 19--25 18--26  2--27 26--27
## [31]  2--28  8--28 18--28 26--28 27--28  2--29  9--29 21--29 11--30 19--30
## [41] 22--30 25--30  8--31 20--31 29--31 18--32 10--33 14--33 13--34 15--34
## [51] 17--34 22--34 15--35 34--35 30--36  2--37 21--37 24--37  9--38 15--38
## [61] 17--38 22--38 34--38 35--38 37--38 15--39 17--39 21--39 34--39 37--40
## [71]  1--41  8--41 15--41 16--41 34--41 37--41 38--41  2--42 10--42 14--42
## + ... omitted several edges
  1. Are there any particular aspects of your visualization to which you would like to bring attention?
  1. What do you think the data, and your visualization, shows?
# Community Plot
wc <- cluster_walktrap(g)
modularity(wc)
## [1] 0.4888454
membership(wc)
##  [1] 2 1 2 3 3 1 1 1 3 1 2 3 2 1 2 3 2 1 3 1 2 3 1 3 3 1 1 1 1 3 1 1 4 2 2
## [36] 3 3 2 2 1 2 1 2 2 2 3 2 2 1 2 2 3 2 2 1 3 1 1 2 3 4 2
g$name    <- "Undirected social network of frequent associations between 62 dolphins"
tkplot(g, vertex.color=membership(wc),
     layout = layout.fruchterman.reingold, 
     main = g$name,
     vertex.label = V(g)$name,
     vertex.size = 9,
     vertex.color= V(g)$color,
     vertex.frame.color= "white",
     vertex.label.color = "black",
     vertex.label.family = "sans",
     edge.width=E(g)$weight, 
     edge.color="black"
     )
## [1] 1

GRAPH PARAMETERS:

# Edge List
gl <- as_edgelist(g, names = TRUE)
gl
##        [,1] [,2]
##   [1,]    4    9
##   [2,]    6   10
##   [3,]    7   10
##   [4,]    1   11
##   [5,]    3   11
##   [6,]    6   14
##   [7,]    7   14
##   [8,]   10   14
##   [9,]    1   15
##  [10,]    4   15
##  [11,]    1   16
##  [12,]   15   17
##  [13,]    2   18
##  [14,]    7   18
##  [15,]   10   18
##  [16,]   14   18
##  [17,]   16   19
##  [18,]    2   20
##  [19,]    8   20
##  [20,]    9   21
##  [21,]   17   21
##  [22,]   19   21
##  [23,]   19   22
##  [24,]   18   23
##  [25,]   15   25
##  [26,]   16   25
##  [27,]   19   25
##  [28,]   18   26
##  [29,]    2   27
##  [30,]   26   27
##  [31,]    2   28
##  [32,]    8   28
##  [33,]   18   28
##  [34,]   26   28
##  [35,]   27   28
##  [36,]    2   29
##  [37,]    9   29
##  [38,]   21   29
##  [39,]   11   30
##  [40,]   19   30
##  [41,]   22   30
##  [42,]   25   30
##  [43,]    8   31
##  [44,]   20   31
##  [45,]   29   31
##  [46,]   18   32
##  [47,]   10   33
##  [48,]   14   33
##  [49,]   13   34
##  [50,]   15   34
##  [51,]   17   34
##  [52,]   22   34
##  [53,]   15   35
##  [54,]   34   35
##  [55,]   30   36
##  [56,]    2   37
##  [57,]   21   37
##  [58,]   24   37
##  [59,]    9   38
##  [60,]   15   38
##  [61,]   17   38
##  [62,]   22   38
##  [63,]   34   38
##  [64,]   35   38
##  [65,]   37   38
##  [66,]   15   39
##  [67,]   17   39
##  [68,]   21   39
##  [69,]   34   39
##  [70,]   37   40
##  [71,]    1   41
##  [72,]    8   41
##  [73,]   15   41
##  [74,]   16   41
##  [75,]   34   41
##  [76,]   37   41
##  [77,]   38   41
##  [78,]    2   42
##  [79,]   10   42
##  [80,]   14   42
##  [81,]    1   43
##  [82,]    3   43
##  [83,]   11   43
##  [84,]   31   43
##  [85,]   15   44
##  [86,]   30   44
##  [87,]   34   44
##  [88,]   38   44
##  [89,]   39   44
##  [90,]    3   45
##  [91,]   21   45
##  [92,]   35   45
##  [93,]   39   45
##  [94,]    9   46
##  [95,]   16   46
##  [96,]   19   46
##  [97,]   22   46
##  [98,]   24   46
##  [99,]   25   46
## [100,]   30   46
## [101,]   38   46
## [102,]   44   47
## [103,]    1   48
## [104,]   11   48
## [105,]   21   48
## [106,]   29   48
## [107,]   31   48
## [108,]   43   48
## [109,]   35   50
## [110,]   47   50
## [111,]   15   51
## [112,]   17   51
## [113,]   21   51
## [114,]   34   51
## [115,]   43   51
## [116,]   46   51
## [117,]    5   52
## [118,]   12   52
## [119,]   19   52
## [120,]   22   52
## [121,]   24   52
## [122,]   25   52
## [123,]   30   52
## [124,]   46   52
## [125,]   51   52
## [126,]   15   53
## [127,]   30   53
## [128,]   39   53
## [129,]   41   53
## [130,]   44   54
## [131,]    2   55
## [132,]    7   55
## [133,]    8   55
## [134,]   14   55
## [135,]   20   55
## [136,]   42   55
## [137,]   16   56
## [138,]   52   56
## [139,]    6   57
## [140,]    7   57
## [141,]    6   58
## [142,]    7   58
## [143,]   10   58
## [144,]   14   58
## [145,]   18   58
## [146,]   40   58
## [147,]   42   58
## [148,]   49   58
## [149,]   55   58
## [150,]   39   59
## [151,]    4   60
## [152,]    9   60
## [153,]   16   60
## [154,]   37   60
## [155,]   46   60
## [156,]   33   61
## [157,]    3   62
## [158,]   38   62
## [159,]   54   62

closeness

The closeness centrality of a vertex is defined by the inverse of the average length of the shortest paths to/from all the other vertices in the graph:

1/sum( d(v,i), i != v)

closeness(g)
##  [1] 0.005681818 0.006097561 0.004629630 0.005050505 0.004081633
##  [6] 0.003906250 0.004385965 0.005988024 0.005952381 0.004132231
## [11] 0.005128205 0.004081633 0.004405286 0.004444444 0.006172840
## [16] 0.005555556 0.005405405 0.005076142 0.005524862 0.005181347
## [21] 0.006410256 0.005464481 0.003891051 0.005464481 0.005128205
## [26] 0.004184100 0.004545455 0.005181347 0.005988024 0.005291005
## [31] 0.005291005 0.003891051 0.003546099 0.005988024 0.005181347
## [36] 0.004016064 0.006849315 0.006535948 0.005405405 0.005494505
## [41] 0.006622517 0.004878049 0.005405405 0.005524862 0.005102041
## [46] 0.005681818 0.004201681 0.005555556 0.003816794 0.004048583
## [51] 0.005747126 0.005405405 0.005617978 0.004255319 0.005319149
## [56] 0.004444444 0.003496503 0.004950495 0.004081633 0.005617978
## [61] 0.002923977 0.004950495

Betweeness

The vertex and edge betweenness are (roughly) defined by the number of geodesics (shortest paths) going through a vertex or an edge.

betweenness(g)
##  [1]  34.921151 390.383717  16.603247   4.344048   0.000000   8.015949
##  [7]  53.751742 216.376673  40.929300  38.236716  29.448398   0.000000
## [13]   0.000000  96.708781 113.408769  60.924764   6.047619 209.169298
## [19]  27.184466  24.365341 187.841704  23.242197   0.000000  77.194498
## [25]  13.510970   3.008730   7.983333  53.503455 122.165227 119.918587
## [31]  60.482343   0.000000  60.000000 104.614585  59.831410   0.000000
## [37] 454.274069 253.582713  82.994597 129.045705 261.963619  42.550429
## [43]  53.359052 114.980006  22.029185  74.426906   5.505495  42.458701
## [49]   0.000000   1.700000  61.142194 154.959376  35.198851   2.183333
## [55] 181.392614   1.605769   0.250000 154.094571   0.000000  37.208978
## [61]   0.000000  25.976818