Statistical analysis of networks generated from exchangeable network models have been extensively studied in the literature. One primary property of exchangeable network models is the conditional independence of edge formation. In this work, we extend the framework of network formation to include dependent edges with emphasis on generating networks with all five properties of sparsity, small-world, community structure, power-law degree distribution, and transitivity or high triangle count. We propose a class of models, called as Transitive Inhomogeneous Erdos-Renyi (TIER) models, which we show has all five properties. We also perform inferential tasks, such as, parameter estimation, community detection, and change-point detection using networks generated from TIER models. We validate our results using simulation studies too. If time permits, we would talk about some recent developments on estimation of number of communities using Bethe Hessian matrices.