In this paper, we propose that when a random network graph model that prefers to close two-hop chains and transform them to triangles as part of link formation. We hypothesize that such a model would generate random network graphs with high clustering coefficients and a larger variation in node degree, compared to that of the well-known Erdos-Renyi (ER) model. We refer to the proposed model as two-hop neighbor preference (THNP)-model that prefers to pair a node with any of its two-hop neighbors

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... rather than to an arbitrary node. The probability of link formation is still governed by the formulation used to generate links in the ER model. We observe the THNP-model to generate random network graphs wherein the clustering coefficient of a node decreases with increase in node degree (resembling closely to several of the realworld network graphs), and the graphs still exhibit a Poisson-style distribution for the node degree and path length.