Efficient network structures with separable heterogeneous connection costs

We introduce a heterogeneous connection model for network formation to capture the effect of cost heterogeneity on the structure of efficient networks. In the proposed model, connection costs are assumed to be separable, which means the total connection cost for each agent is uniquely proportional to its degree. For these sets of networks, we provide the analytical solution for the efficient network as a function of connection costs and benefits. We show that the efficient network exhibits a core–periphery structure. Moreover, for a given link density, we find a lower bound for the clustering coefficient of the efficient network, and compare it to that of the Erdős–Rényi random networks.