Integration in Social Networks

TL;DR

This paper introduces the concept of $k$-integration to measure equality of opportunity in social networks, analyzing how network structure affects access to opportunities and proposing methods to achieve $k$-integration efficiently.

Contribution

It defines $k$-integration as a new measure of opportunity equality and provides formulas for the minimum number of bridges needed to achieve it in social networks.

Findings

Minimum bridges depend linearly on component size for $k=2$.

For $k \,\geq\, 3$, the minimum number of bridges is independent of component size.

The approach offers a simple way to compare social network equality.

Abstract

We propose the notion of $k$-integration as a measure of equality of opportunity in social networks. A social network is $k$-integrated if there is a path of length at most $k$ between any two individuals, thus guaranteeing that everybody has the same network opportunities to find a job, a romantic partner, or valuable information. We compute the minimum number of bridges (i.e. edges between nodes belonging to different components) or central nodes (those which are endpoints to a bridge) required to ensure $k$-integration. The answer depends only linearly on the size of each component for $k=2$, and does not depend on the size of each component for $k \geq 3$. Our findings provide a simple and intuitive way to compare the equality of opportunity of real-life social networks.