Finding and evaluating community structure in networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 69, Issue 2 2, 2004, Pages

  Newman, M E J ^a,b   Girvan, M ^b,c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b SANTA FE INSTITUTE   (United States)

^c Cornell University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER NETWORKS; COMPUTER SCIENCE; ECOSYSTEMS; GRAPH THEORY; HEURISTIC METHODS; HIERARCHICAL SYSTEMS; ITERATIVE METHODS; MATHEMATICAL MODELS; PARALLEL PROCESSING SYSTEMS; PROGRAM PROCESSORS; SOCIAL SCIENCES COMPUTING; WEBSITES;

AGGLOMERATIVE METHOD; COMMUNITY STRUCTURE; GRAPH PARTITIONING; HIERARCHICAL CLUSTERING;

LARGE SCALE SYSTEMS;

EID: 37649028224     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.69.026113     Document Type: Article

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48. Following the publication of Ref. [25], the algorithm has been implemented in the software packages UCISET and NETDRAW and in the open-source network library JUNG. (See http://www.analytictech.com/ and http://jung. sourceforge.net/.)
49. In fact, we have tried counting each traversal separately, but this method gives extremely poor results, confirming our intuition that this would not be a good betweenness measure.
50. ij - the same edge should not appear both above and below the diagonal. Alternatively, an edge linking communities i and j can be split, half-and-half, between the ij and ji elements, which has the advantage of making the matrix symmetric. Either way, there are a number of factors of 2 in the calculation that must be watched carefully, lest they escape one's attention and make mischief.
51. In Ref. [34], the measure was normalized by dividing by its value on a network with perfect mixing, so that we always get 1 for such a network. We find, however, that doing this in the present case masks some of the useful information to be gained from the value of Q, and hence that it is better to use the unnormalized measure. In general, this unnormalized measure will not reach a value of 1, even on a perfectly mixed network.
52. The graph is one of the test graphs from the graph drawing competition held in conjunction with the Symposium on Graph Drawing, Berkeley, California, September 18-20, 1996.