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Randi Griffin
10/06/09 1:35pm


I have written a program that simulates spreading on networks, and I am trying to explore the way in which community substructure (as measured by community modularity) effects the efficiency of spreading.

What I am trying to do now is generate networks that span the range of community modularity from cm=0 to cm=1 (for the partition, I am using "CommunityStructureAssignment"), but I have run into a problem: I can't come up with a network that has a community modularity of greater that 0.5!

From my understanding of the metric, it should be straightforward to design a network that has cm=1; it should be a network that has completely disconnected subgroups, such that it is not a connected graph. Here is a graph g=Graph:<6,6,Undirected>


g = FromAdjacencyMatrix[{{0, 1, 1, 0, 0, 0}, {1, 0, 1, 0, 0, 0}, {1,
1, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 1}, {0, 0, 0, 1, 0, 1}, {0, 0, 0,
1, 1, 0}}];
CommunityModularity[g, CommunityStructureAssignment[g]]



I can't understand why the community modularity for this network is not 1, and I am clueless as to what a network of cm=1 would look like (if not like this one). Any help is greatly appreciated!


Attachment: Untitled-1.nb, URL: ,
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