Properties of a Projected Network of a Bipartite Network

Abstract: Bipartite Graph is often a realistic model of complex networks where two different sets of entities are involved and relationship exist only two entities belonging to two different sets. Examples include the user-item relationship of a recommender system, actor-movie relationship of an online movie database systems. One way to compress a bipartite graph is to take unweighted or weighted one mode projection of one side vertices. Properties of this projected network are extremely important in many practical situations (say the selection process of influencing nodes for viral marketing). In this paper, we have studied the topological properties for projected network and some theoretical results are proved including the presence of cliques, connectedness for unweighted projection and maximum edge weight for weighted projected network.