Intersection-Link Representations of Graphs

TL;DR

This paper introduces intersection-link representations for graphs with dense subgraphs, using geometric objects and intersections to visualize complex structures, and studies a planarity concept called Clique Planarity.

Contribution

It proposes a novel intersection-link representation model for graphs with dense subgraphs and explores the planarity properties specific to clique-based dense subgraph structures.

Findings

Defined intersection-link representations for dense subgraphs

Introduced the concept of Clique Planarity

Analyzed planarity conditions for these representations

Abstract

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and in which each edge $(u,v)$ is represented by the intersection between $R(u)$ and $R(v)$ if it belongs to a dense subgraph or by a curve connecting the boundaries of $R(u)$ and $R(v)$ otherwise. We study a notion of planarity, called Clique Planarity, for intersection-link representations of graphs in which the dense subgraphs are cliques.