Individual-centered partial information in social networks

TL;DR

This paper introduces a framework for community detection in social networks based on individuals' local views, deriving spectral algorithms and a new centrality measure that leverage partial network information.

Contribution

It develops a partial information framework for social networks, proposes spectral algorithms for community detection, and introduces a novel centrality measure based on local views.

Findings

Spectral algorithms achieve consistency in community detection under partial information.

The new centrality measure effectively captures individual importance in global structure.

Algorithms perform well on simulated and real networks, outperforming some existing measures.

Abstract

In statistical network analysis, we often assume either the full network is available or multiple subgraphs can be sampled to estimate various global properties of the network. However, in a real social network, people frequently make decisions based on their local view of the network alone. Here, we consider a partial information framework that characterizes the local network centered at a given individual by path length $L$ and gives rise to a partial adjacency matrix. Under $L=2$, we focus on the problem of (global) community detection using the popular stochastic block model (SBM) and its degree-corrected variant (DCSBM). We derive theoretical properties of the eigenvalues and eigenvectors from the signal term of the partial adjacency matrix and propose new spectral-based community detection algorithms that achieve consistency under appropriate conditions. Our analysis also allows us to propose a new centrality measure that assesses the importance of an individual's partial information in determining global community structure. Using simulated and real networks, we demonstrate the performance of our algorithms and compare our centrality measure with other popular alternatives to show it captures unique nodal information. Our results illustrate that the partial information framework enables us to compare the viewpoints of different individuals regarding the global structure.