Comparing clusterings---an information based distance
Journal of Multivariate Analysis
Identification and evaluation of weak community structures in networks
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
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Complex network analysis involves the study of the properties of various real world networks. In this broad field, research on community structures forms an important sub area. The strength of community structure is typically quantified by the modularity measure. The measure is based on summing the differences in actual and expected fraction of edges per community (across all communities in the network), whereby the latter is computed based on randomizing the edges subjected to certain constrains. In this paper, we investigate the differences between two commonly used definitions of modularity and highlight one of them as inadequate for quantifying the strength of community structures. We first show this by mathematical proving. We then investigate the empirical differences by developing and testing two variants of a community detection algorithm whereby the variants differ based on their modularity definitions. We observe varying differences in detection accuracy when applying the variants on artificially generated networks. For networks with strong community structures, we show that sensible results are still obtainable with the inadequate measure, which explains why this issue did not come to light previously.