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## [igraph] Relation between network's clustering coefficient and density

**From**: |
capitano . nemo |

**Subject**: |
[igraph] Relation between network's clustering coefficient and density |

**Date**: |
Wed, 18 Nov 2015 19:46:35 +0000 |

**User-agent**: |
Roundcube Webmail |

`From a undirected friendship network with N nodes I have extracted N
``neighboring graphs of order 1 with make_ego_graph(). For each resulting
``graph I calculated density and transitivity. My question is, shuld the
``two statistics be perfectly correlated in social networks? Is it trivial
``to present both statistics?
`

`I run a simulation with erdos.renyi.game() and in fact got almost
``perfect correlation:
`
graph_clustering_coeff <- numeric()
graph_density <- numeric()
for(i in seq(0,1,by=.01)) {
print(i)
g <- erdos.renyi.game(100, i)
graph_clustering_coeff <- c(graph_clustering_coeff, transitivity(g))
graph_density <- c(graph_density, graph.density(g))
}
cor.test(graph_clustering_coeff, graph_density)
# Pearson's product-moment
# correlation
#
# data: graph_clustering_coeff and graph_density
# t = 600.36, df = 98, p-value <
# 2.2e-16
# alternative hypothesis: true correlation is not equal to 0
# 95 percent confidence interval:
# 0.9997976 0.9999087
# sample estimates:
# cor
# 0.9998641
plot(graph_clustering_coeff, graph_density)
Thanks!
Francesco

**[igraph] Relation between network's clustering coefficient and density**,
*capitano . nemo* **<=**