کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4599188 | 1631122 | 2015 | 18 صفحه PDF | دانلود رایگان |
There is an exact relation between the spectra of modularity matrices introduced in social network analysis and the χ2χ2 statistic. We investigate a weighted graph with the main interest being when the hypothesis of independent attachment of the vertices is rejected, and we look for clusters of vertices with higher inter-cluster relations than expected under the hypothesis of independence. In this context, we give a sufficient condition for a weighted, and a sufficient and necessary condition for an unweighted graph to have at least one positive eigenvalue in its modularity or normalized modularity spectrum, which guarantees a community structure with more than one cluster. This property has important implications for the isoperimetric inequality, the symmetric maximal correlation, and the Newman–Girvan modularity.
Journal: Linear Algebra and its Applications - Volume 473, 15 May 2015, Pages 359–376