Multiresolution network models

TL;DR

This paper introduces multiresolution network models that analyze social networks at multiple scales, enabling comparisons across different-sized graphs and capturing community structures effectively.

Contribution

It proposes a novel class of models that represent multi-scale network structures and are projective, addressing limitations of existing single-scale methods.

Findings

Model effectively captures community structures.

Enables comparison across graphs of different sizes.

Demonstrated utility with household relation data.

Abstract

Many existing statistical and machine learning tools for social network analysis focus on a single level of analysis. Methods designed for clustering optimize a global partition of the graph, whereas projection based approaches (e.g. the latent space model in the statistics literature) represent in rich detail the roles of individuals. Many pertinent questions in sociology and economics, however, span multiple scales of analysis. Further, many questions involve comparisons across disconnected graphs that will, inevitably be of different sizes, either due to missing data or the inherent heterogeneity in real-world networks. We propose a class of network models that represent network structure on multiple scales and facilitate comparison across graphs with different numbers of individuals. These models differentially invest modeling effort within subgraphs of high density, often termed communities, while maintaining a parsimonious structure between said subgraphs. We show that our model class is projective, highlighting an ongoing discussion in the social network modeling literature on the dependence of inference paradigms on the size of the observed graph. We illustrate the utility of our method using data on household relations from Karnataka, India.