A Hybrid Graph-drawing Algorithm for Large, Naturally-clustered, Disconnected Graphs

TL;DR

This paper introduces a hybrid graph-drawing algorithm designed to effectively layout large, naturally-clustered, disconnected graphs, addressing scalability issues of existing force-based methods, with a detailed complexity analysis.

Contribution

The paper presents a novel hybrid algorithm that combines known procedures to improve scalability for large, disconnected, clustered graphs, with a comprehensive complexity derivation.

Findings

Hybrid algorithm successfully handles large, disconnected graphs.

Time complexity of the hybrid algorithm is $O(|V|^3)$.

Addresses limitations of force-based graph drawing methods.

Abstract

In this paper, we present a hybrid graph-drawing algorithm (GDA) for layouting large, naturally-clustered, disconnected graphs. We called it a hybrid algorithm because it is an implementation of a series of already known graph-drawing and graph-theoretic procedures. We remedy in this hybrid the problematic nature of the current force-based GDA which has the inability to scale to large, naturally-clustered, and disconnected graphs. These kinds of graph usually model the complex inter-relationships among entities in social, biological, natural, and artificial networks. Obviously, the hybrid runs longer than the current GDAs. By using two extreme cases of graphs as inputs, we present in this paper the derivation of the time complexity of the hybrid which we found to be $O(|\V|^3)$.