Energy Models for Graph Clustering

Abstract

The cluster structure of many real-world graphs is of great interest, as the clusters may correspond e.g. to communities in social networks or to cohesive modules in software systems. Layouts can naturally represent the cluster structure of graphs by grouping densely connected nodes and separating sparsely connected nodes. This article introduces two energy models whose minimum energy layouts represent the cluster structure, one based on repulsion between nodes (like most existing energy models) and one based on repulsion between edges. The latter model is not biased towards grouping nodes with high degrees, and is thus more appropriate for the many real-world graphs with right-skewed degree distributions. The two energy models are shown to be closely related to widely used quality criteria for graph clusterings -namely the density of the cut, Shi and Malik's normalized cut, and Newman's modularity -and to objective functions optimized by eigenvector-based graph drawing methods.

Graphical interface of the <i>SCImago Journal and Country Rank</i>: an interactive approach to accessing bibliometric information

“…Although Noack (2007) shows a certain reluctance to regard as appropriate the use of multi-scale strategies in combination with LinLog energy models, the results obtained in the The results obtained in the present study suggest that the use of multi-scale strategies in combination with LinLog energy models, is a very efficient method to achieve high quality layouts for large networks present study suggest that the procedure is indeed a very efficient method with which to achieve high quality layouts for large networks. The nodes are represented graphically by discs whose size (their area) encodes the value of whichever bibliometric indicator that the user has selected (SJR, documents, references, citations…).…”

“…We started by implementing the force-directed algorithm using the edge-repulsion energy model proposed by Noack (2007).…”

On the Likelihood of an Equivalence

“…star-like structures) are not seen as clusters and are thus decomposed into single nodes. A different approach recently proposed by Noack [11] seems to overcome this behavior. In Noack's approach, a graph is seen as a metaphor of a mechanical system where each node is a particle whose "position" is determined by the "forces" acting on it.…”

Stakeholders' social interaction in requirements engineering of open source software

“…In addition to providing a visual representation of the network, CCVisu uses LinLog energy model [145], a visual clustering technique, and produces optimal layouts that provide separation of cohesive sub-graphs with interpretable distances. CCVisu also provides search and customized zoom-in facilities that help us find and analyze structural hole positions in a large network.…”