The domination number of on-line social networks and random geometric graphs

TL;DR

This paper investigates the domination number in online social networks and random geometric graphs, deriving asymptotic bounds and validating them with real-world Facebook data.

Contribution

It provides the first rigorous asymptotic bounds for the domination number in a stochastic geometric network model and real-world social network data.

Findings

Sublinear bounds for domination number in the geometric model

Sublinear bounds for Facebook network data

Correlation between model predictions and real data

Abstract

We consider the domination number for on-line social networks, both in a stochastic network model, and for real-world, networked data. Asymptotic sublinear bounds are rigorously derived for the domination number of graphs generated by the memoryless geometric protean random graph model. We establish sublinear bounds for the domination number of graphs in the Facebook 100 data set, and these bounds are well-correlated with those predicted by the stochastic model. In addition, we derive the asymptotic value of the domination number in classical random geometric graphs.