Journal of Statistical Physics (2020) 179:1–32 https://doi.org/10.1007/s10955-020-02517-z Generating Graphs by Creating Associative and Random Links Between Existing Nodes Muhammad Irfan Yousuf 1 · Suhyun Kim 1 Received: 1 August 2019 / Accepted: 27 February 2020 / Published online: 6 March 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract The study and analysis of real-world social, communication, information and citation net- works 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 net- work 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 generat- ing 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. Keywords Graph algorithms · Big graphs · Generative models 1 Introduction Complex networks are neither purely regular nor purely random. The non-trivial features of complex networks have been witnessed in the empirical studies [1,22] of real-world networks that include heavy-tailed degree distribution, small-world phenomenon and high clustering coefficient, to name a few. Most social, informational, biological and technical networks are Communicated by Irene Giardina. B Suhyun Kim suhyun_kim@kist.re.kr Muhammad Irfan Yousuf irfan@kist.re.kr 1 Imaging Media Research Center, Korea Institute of Science and Technology, Seoul, Republic of Korea 123