Orca Reduction and ContrAction Graph Clustering

Abstract

Abstract. During the last years, a wide range of huge networks has been made available to researchers. The discovery of natural groups, a task called graph clustering, in such datasets is a challenge arising in many applications such as the analysis of neural, social, and communication networks. We here present Orca, a new graph clustering algorithm, which operates locally and hierarchically contracts the input. In contrast to most existing graph clustering algorithms, which operate globally, Orca is able to cluster inputs with hundreds of millions of edges in less than 2.5 hours, identifying clusterings with measurably high quality. Our approach explicitly avoids maximizing any single index value such as modularity, but instead relies on simple and sound structural operations. We present and discuss the Orca algorithm and evaluate its performance with respect to both clustering quality and running time, compared to other graph clustering algorithms.

Dynamic graph clustering combining modularity and smoothness

“…The literature on static modularity-maximization is quite broad. We omit a comprehensive review at this point and refer the reader to (Brandes, Delling, Gaertler, Görke, Höfer, Nikoloski, and Wagner 2008;Fortunato 2009;Schaeffer 2007) for overviews, further references and comparisons to other clustering techniques. Spectral methods, e.g., (White and Smyth 2005), and techniques based on random walks (Pons and Latapy 2006;van Dongen 2000), do not lend themselves well to dynamization due to their non-continuous nature.…”

“…Generally, a partition (i.e., a clustering) of the set of nodes is sought, and the size of the partition is a priori unknown. A plethora of formalizations for what a good clustering is exist, good overviews are, e.g., (Brandes and Erlebach 2005;Fortunato 2009). In this work we set our focus on the quality function modularity, coined by Newman and Girvan (2004), which has proven itself feasible and reliable in practice, especially as the target function for a maximization approach (see (Brandes, Delling, Gaertler, Görke, Höfer, Nikoloski, and Wagner 2008) for further references) that follows the paradigm of parameter-free community discovery (Keogh, Lonardi, and Ratanamahatana 2004).…”

“…Iteratively clustering snapshots of a dynamic graph from scratch with a static method has several disadvantages: First, runtime cannot be neglected for large instances or environments where computing power is limited (Schaeffer, Marinoni, Särelä, and Nikander 2006), even though very fast clustering methods have been proposed recently (Blondel, Guillaume, Lambiotte, and Lefebvre 2008;Delling, Görke, Schulz, and Wagner 2009). Second, heuristics for the NP-hard (Brandes, Delling, Gaertler, Görke, Höfer, Nikoloski, and Wagner 2008) optimization of modularity suffer from local optima-this might be avoided by dynamically maintaining a good solution.…”

Modularity-Driven Clustering of Dynamic Graphs

“…In later plots we use selected random instances, however, descriptions apply to all such graphs. 7 EMail Graph G e . The network of email contacts at the department of computer science at KIT is an ever-changing graph with an inherent clustering: Workgroups and projects cause increased communication.…”

“…Iteratively clustering snapshots of a dynamic graph from scratch with a static method has several disadvantages: First, runtime cannot be neglected for large instances or environments where computing power is limited [5], even though very fast clustering methods have been proposed recently [6,7]. Second, heuristics for the NP-hard [1] optimization of modularity suffer from local optima-this might be avoided by dynamically maintaining a good solution.…”