Emergence of network communities driven by local rules

TL;DR

This paper demonstrates through simulations that network communities can emerge from local rules without the need for node heterogeneity, introducing the Ramsey community number as a key measure.

Contribution

It introduces the Ramsey community number and shows that local rules can lead to community emergence, challenging the idea that heterogeneity is necessary.

Findings

Networks with local rules have finite Ramsey community numbers.

Randomized networks do not exhibit emergent communities.

Community emergence is an emergent property of networks evolving with local rules.

Abstract

Natural systems are modeled by networks with nodes and links. Often the nodes are segregated into communities with different connectivity patterns. Node heterogeneity such as political affiliation in social networks or biological function in gene networks are highlighted as key factors driving the segregation of nodes into communities. Here, by means of numerical simulations, I show that node heterogeneity is not a necessary requirement. To this end I introduce the Ramsey community number, $r_ \kappa$, the minimum graph size that warranties the emergence of network communities with almost certainty. Using the stochastic block model and Infomap methods for community detection, I show that networks generated by local rules have finite $r_ \kappa$ values while their randomized versions do not have emergent communities. I conjecture that network communities are an emergent property of networks evolving with local rules.