Comparison of Centrality-Based Planarisation for 2.5D Graph Drawing

Planarisation of graphs is a well studied research problem in Graph Theory and has important applications in Graph Drawing to draw non-planar graphs with as few crossings as possible. However, the problem of finding the maximum vertex (or edge) induced planar subgraph NP-hard. Centrality index is one of the important concepts in Network Analysis for analysing the importance of actors in the social network. In this paper, we present centrality-based planarisation algorithms with four variations: vertex addition, vertex deletion, edge addition and edge deletion. Our research is inspired by domain specific problem of drawing a social network in 2.5 dimensions which emphasizes important actors by placing on the top layer. More specifically, we compare five different vertex (or edge) centralities in order to investigate the impact of different vertex (or edge) orderings on the resulting maximal induced planar subgraphs. We present extensive experimental results using both the standard Graph Drawing test suites and popular network models. We further extend our centrality-based planarisation algorithm to compute the thickness (both vertex thickness and edge thickness) of graphs.