Mathematical Modeling of Social Networks: A Probabilistic Approach to Explore Relationship in Social Networks

Abstract

Online Social Networks system is based on the relationship among members of social networks. Communication among nodes influences their relationship. Relationship among nodes may be visible or invisible. The relationship among members of social networks passes through three stages of life cycles which are primary stage, secondary stage and termination Stage. Primary stages are those stages in which the relationship among two or more nodes are established. This relationship may be direct (i.e., one to one or one to many) and indirect (i.e., mutual relation, virtual relation etc.). Secondary stages are those stages in which the communication among nodes (i.e. members of social networks) starts. But there is always uncertainty related to communication among nodes of social networks. There may be chances that communication among nodes with each other may be for gap of short duration, medium duration or long duration. A sender may send a message to different others members of social networks but he may not get certain response on a message. Types of response on a message establishes the different kinds of relationship. In the present paper the authors made a study on probabilistic approach to establish different types of relationship among nodes on the basis of their response and with their activity. The authors also applied co-relation theory to establish different types of relationship like positive, negative, no relationship and perfect relationship.