a novel centrality method for weighted networks based on the kirchhoff polynomial论文.pdf

Pattern Recognition Letters 58 (2015) 51–60 Contents lists available at ScienceDirect Pattern Recognition Letters journal homepage: /locate/patrec A novel centrality method for weighted networks based on the Kirchhoff polynomial ✩ a b b b,∗ Xingqin Qi , Edgar Fuller , Rong Luo , Cun-quan Zhang a School of Mathematics, Shandong University, Jinan, Shandong Province, 250100, China b Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA a r t i c l e i n f o a b s t r a c t Article history: The measuring of centralities, which determines the importance of vertices in a network, has been one of the Received 23 May 2014 key issues in network analysis. Comparing with various measures developed for unweighted networks, little Available online 11 March 2015 work has been done yet for weighted networks. In this paper, a new centrality measurement, called spanning tree centrality (STC for short), is introduced for weighted networks. The STC score of a vertex v in G is defined as Keywords: Centrality method the number of spanning trees with the vertex v as a cut vertex. We show that STC scores can be calculated by Spanning tree the Kirchhoff polynomial of G. In order to verify the validity of STC, we apply it on several benchmark social Weighted network networks and all get satisfied and even be