Cross-Layer Closeness Centrality in Multiplex Social Networks

The centrality measure of nodes gives the influential power of the entities in a given network. Closeness centrality measure of a node is the amount to which a node is close to all other nodes. More recently, centrality measures in the multiplex social networks have develops a great interest among researchers. The multiplex social network means the system, which includes multiple networks in the form of layers, and each layer belongs to different types of the association between nodes. Here, we present a new formulation to compute the closeness centrality of nodes for the multiplex social networks or multi-layer networks. There are numerals of approaches defined to find the closeness centrality of the node in a single layer network, the problem for computing the closeness centrality measure for the multiplex networks node is still open. With this, we define a new metric called cross-layer closeness centrality (CCC) for the multiplex social networks. The CCC is the measure, which computes closeness degree of a node to every other node of the multiplex network.