The groupies of random multipartite graphs

TL;DR

This paper investigates the properties of 'groupies' in random multipartite graphs, extending prior research on bipartite graphs by analyzing how vertices with higher-than-average neighbor degrees behave in these complex structures.

Contribution

It introduces a comprehensive analysis of groupies in random multipartite graphs, generalizing earlier bipartite graph results to more complex multipartite settings.

Findings

Characterization of groupie distribution in multipartite graphs

Extension of bipartite graph results to multipartite cases

Insights into degree behavior in random multipartite structures

Abstract

If a vertex $v$ in a graph $G$ has degree larger than the average of the degrees of its neighbors, we call it a groupie in $G$. In the current work, we study the behavior of groupie in random multipartite graphs with the link probability between sets of nodes fixed. Our results extend the previous ones on random (bipartite) graphs.