Ali Hojjat - Department of Industrial Engineering, Tarbiat Modares University, Tehran, Iran
Ghazaleh Haddad - Department of Industrial Engineering, Tarbiat Modares University, Tehran, Iran
Mehrdad Kargari - Department of Industrial Engineering, Tarbiat Modares University, Tehran, Iran

The world around us consists of individuals, objects, and environments that have different relationships with each other. The result of these communications is various networks that part of them are bipartite networks. Many studies have been conducted on the investigation of important members in networks, such as centrality measures, but less attention has been paid to bipartite graphs. On the other hand, one of the most important aspects of network analysis is the detection and extraction of communities that arise in the structure of this network. For these reasons, we have introduced a measure called H.H to identify effective nodes in community formation in the one-mode projection of a bipartite graph. The three main parameters that influence this measure are the size of the community formed, the effect of each node in the formation of that community and the number of communities that the node had effective in its formation. The results of this paper show the differences and similarities of this measure with other centralities (Eigenvector centrality, closeness centrality, betweenness centrality, degree centrality). By H.H score we can find important nodes that have been effective in forming a community, and by removing these nodes, communities can be eliminated, and on the other hand, by adding nodes with a good H.H score, more important and stronger communities can be created in the one-mode projection of a bipartite graph. This issue has not been addressed by any of the existing centralities and this measure has sufficient independence to represent the important nodes in the formation of the communities. Experimental validation of the proposed measure is carried out on two real-world datasets: Southern Women Network and Person-Crime Network.)

bipartite graph, community detection, complex network, network analysis)