Efficient Integration in Multi-Community Networks

We study structures for efficient integration of multi-community networks where building bridges across communities incur an additional link cost compared to links within a community. Building on the connections models with direct link cost and direct and indirect benefits, we show that the efficient structure for homogeneous cost and benefit parameters, and for communities of arbitrary size, always has a diameter no greater than 3. We further show that if the internal cost is not small enough to justify a full graph for each community, integration always follows one of these two structures: Either a single star, or a new structure we introduce in this paper, called parallel-hyperstar, which is a special multi-core/periphery structure with parallel links among core nodes of different communities. We offer cost and benefit conditions where each structure is efficient and discuss the stability conditions of those structures.

Source: papers.ssrn.com