Distribution-Free Models of Social Networks

TL;DR

This paper surveys recent robust, distribution-free models of social networks that focus on deterministic combinatorial structures, providing insights into their definitions, empirical relevance, and structural properties.

Contribution

It introduces and discusses distribution-free models of social networks that emphasize deterministic structures over probabilistic ones, advancing understanding of network robustness.

Findings

Distribution-free models better capture empirical social network structures.

Structural and algorithmic properties of these models are well-understood.

These models provide a robust alternative to traditional generative models.

Abstract

The structure of large-scale social networks has predominantly been articulated using generative models, a form of average-case analysis. This chapter surveys recent proposals of more robust models of such networks. These models posit deterministic and empirically supported combinatorial structure rather than a specific probability distribution. We discuss the formal definitions of these models and how they relate to empirical observations in social networks, as well as the known structural and algorithmic results for the corresponding graph classes.