Generating Graphs by Creating Associative and Random Links Between Existing Nodes

The study and analysis of real-world social, communication, information and citation networks for understanding their structure and identifying interesting patterns have cultivated the need for designing generative models for such networks. A generative model generates an artificial but a realistic-looking network with the same characteristics as that of a real network under study. In this paper, we propose a new generative model for generating realistic networks. Our proposed model is a blend of three key ideas namely preferential attachment, associativity of social links and randomness in real networks. We present a framework that first tests these ideas separately and then blends them into a mixed model based on the idea that a real-world graph could be formed by a mixture of these concepts. Our model can be used for generating static as well as time evolving graphs and this feature distinguishes it from previous approaches. We compare our model with previous methods for generating graphs and show that it outperforms in several aspects. We compare our graphs with real-world graphs across many metrics such as degree, clustering coefficient and path length distributions, assortativity, eigenvector centrality and modularity. In addition, we give both qualitative and quantitative results for clarity.