A Novel Centrality for Finding Key Persons in a Social Network by the Bi-Directional Influence Map

Symmetry is one of the important properties of Social networks to indicate the co-existence relationship between two persons, e.g., friendship or kinship. Centrality is an index to measure the importance of vertices/persons within a social network. Many kinds of centrality indices have been proposed to find prominent vertices, such as the eigenvector centrality and PageRank algorithm. PageRank-based algorithms are the most popular approaches to handle this task, since they are more suitable for directed networks, which are common situations in social media. However, the realistic problem in social networks is that the process to find true important persons is very complicated, since we should consider both how the influence of a vertex affects others and how many others follow a given vertex. However, past PageRank-based algorithms can only reflect the importance on the one side and ignore the influence on the other side. In addition, past algorithms only view the transition from one status to the next status as a linear process without considering more complicated situations. In this paper, we develop a novel centrality to find key persons within a social network by a proposed synthesized index which accounts for both the inflow and outflow matrices of a vertex. Besides, we propose different transition functions to represent the relationship from status to status. The empirical studies compare the proposed algorithms with the conventional algorithms and show the differences and flexibility of the proposed algorithm.