Sublinear domination and core\u2013periphery networks

Marios Papachristou

doi:10.1038/s41598-021-94105-8

Abstract

In this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network. We show that instances generated by this model exhibit power law degree distributions, and incorporates small-world phenomena. We also fit our model in a variety of real-world networks.

Highlights

In this paper we devise a generative random network model with core–periphery properties whose core nodes act as sublinear dominators, that is, if the network has n nodes, the core has size o(n) and dominates the entire network
In the context of a social network, the core of the network refers to the individuals that possess a celebrity status in society, such as famous politicians, actors, and athletes, and the rest of the users constitute the periphery of the network
The main concept behind exploiting the core–periphery structure of networks to speed up computational tasks is based on the general idea that intense computational tasks can be performed within the sublinear core and the results can be aggregated to the periphery with relatively low query complexity

Summary

Conclusions

The present paper observes a connection between the core–periphery structure of networks and dominating sets. We devise a simple generative model which facilitates this connection and fit it to real-world data validating our observations. We believe it is worthwhile to explore the algorithmic implications of this connection further

Methods

Findings

Code availability