A Study on Semi-directed Graphs for Social Media Networks

In the literature of graph theory, networks are represented as directed graphs or undirected graphs and a mixed of both combinations. In today's era of computing, networks like brain and facebook that do not belong to any of the mentioned networks category and in fact, it belongs to the combination of both networks which have connections as directed as well as undirected. To represent such networks, semi-directed graphs have been studied in this paper that provides the detailed mathematical fundamentals related to better understand the conceptualization for social media networks. This paper also discusses the suitable matrices analyze for the representation of the graphs. Few new terminologies like incidence number, complete-incidence related to semi-directed graphs and counter isomorphism of semi-directed graphs have been inculcated. A centrality measure, namely incidence centrality, has also been proposed based on incidence number on neighbors in social media networks.