Network Homophily and Graph Theoretical Surroundings

Homophily is a sociological born principle. It asserts that individuals in any 'social' population preferably interact with like individuals. Vertex-colored graphs model finite populations of interacting individuals, where like individuals have the same color. The population exhibits homophily when the coloring correlates with
the graph. What does this mean? One natural answer could be (and has often been given in the literature): Subgraphs induced by the color classes are denser. So, the next question is: Denser than what? In this talk, we will attempt to answer this question by taking a combinatorial statistical approach: the Random Coloring Model. We will corroborate this by making comparisons with the state of the art, some asymptotics and a few new, concrete findings.

This talk is also based on joint work with other colleagues, especially Paolo Giulio Franciosa and Daniele Santoni.