Homophily within and across groups.

Abstract

Homophily-the tendency of individuals to interact with similar others-shapes how networks form and function. Yet existing approaches typically collapse homophily to a single scale, either one parameter for the whole network or one per community, thereby detaching it from other structural features. Here, we introduce a maximum-entropy random graph model that moves beyond these limits, capturing homophily across all social scales in the network, with parameters for each group size. The framework decomposes homophily into within- and across-group contributions, recovering the stochastic block model as a special case. As an exponential-family model, it fits empirical data and enables inference of group-level variation of homophily that aggregate metrics miss. The group-dependence of homophily substantially impacts network percolation thresholds, altering predictions for epidemic spread, information diffusion, and the effectiveness of interventions. Ignoring such heterogeneity risks systematically misjudging connectivity and dynamics in complex systems.