Samuel Thiriot

Thursday 17 November 2016
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example of SII network


The Simple Interconnect Islands (SII) network generator creates networks made of nb.islands islands. Each island is made of a random network of size size.island and having density Every pairs of islands are interconnected by n.inter links.

This random network generator may be used for benchmarking and/or simulation. It creates small-world networks with communities. It does not intends to generate plausible nor realistic networks, but its statistical properties may be easily tuned by playing with its parameters.


  • expected total number of edges (total_links_expected): (nb.islands-1)*nb.islands/2 + nb.islands*size.island*(size.island-1)/2*
  • total number of nodes (totalsize): nb.islands*size.island
  • expected average degree: 2*total_links_expected/totalsize
  • expected density: total_links_expected/(totalsize*(totalsize-1)/2)
  • expected clustering rate into each island: (as in any random network)
  • expected clustering rate in the whole network: (^3 + (n.inter/size.island)^3) / (^2 + (n.inter/size.island)^2)
  • distribution of degree is Poisson-like (sum of the distribution of connectivity for islands).


  • connected as long as is high enough (as in any random network)
  • average path length increase slighly when size.island increase. Average path length decrease when nb.islands increase.
  • islands create areas with strong clustering
  • average short path remains low because of the interconnections between islands.
  • as a consequence, SII networks are small-world according to the Watts&Strogatz 1998 definition.


This R script enable a low-perf generation of SII (requires the igraph package).

This network generator will next be included in the igraph package with a more efficient C version (see for sourcecode.


First open R, load the igraph library, and copy/past the script above:

Generating a SII network:

Display it and observe some of its properties:

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(c) Samuel Thiriot 2012-2016
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