کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4599188 1631122 2015 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spectral properties of modularity matrices
ترجمه فارسی عنوان
خواص طیفی ماتریس های مدولار
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 473, 15 May 2015, Pages 359–376
نویسندگان
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