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Abstract

A social network is a group of individuals having some pattern of interactions between them. Social network analysis is used to study such social structures by identifying local and global patterns, locating influential entities and examining network dynamics. Social networks evolve over time. Individuals create and deactivate social ties, thereby altering the structure of the social network in which they participate. Most of the social networks display patterns of interaction between their elements that are neither purely regular nor purely random. Such networks are called complex networks. Two well-known classes of complex networks are scale-free networks and small-world networks. A number of random graph models are available which can be used to represent these two classes of a complex network effectively. The Barabasi-Albert preferential attachment model generates scale-free networks and the Watts-Strogatz model produces networks having small-world properties. The paper studies Facebook network using the Barabasi-Albert model and the Watts-Strogatz model. The average centralities, the clustering coefficient and the degree-distribution have been obtained for the respective random graph models and then compared with that of the original graph. To enhance this comparative study, the classical Erdos-Renyi random graph model, which generates a purely random graph, has also been used.

Description

Social networks consist of a large number of interacting components. The structure of a social network can be represented by a graph where the nodes represent the components and edges represent the interactions between the components (Carrington et al., 2005). Social networks can be treated as realizations of random variables. Random graph models act as a reference graph for the comparative study of the properties of empirical social networks. Real-world social networks are often complex networks. Such a type of network exhibits a power law degree distribution, a high clustering coefficient and short average path lengths. The study of complex networks is an active area of scientific research. Scale-free networks (Barabasi and Albert, 1999) and small-world networks (Watts and Strogatz, 1998) are the two classes of complex networks characterized by specific structural features.

Keywords

Information Technology Journal, Social network, Complex network, Scale-free networks, Small-world networks, Random graph models, Centrality, Degree distribution, Clustering coefficient