Robert Görke

On Modularity Clustering

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, particularly in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomerative approach.

On finding graph clusterings with maximum modularity

Modularity is a recently introduced quality measure for graph clusterings. It has immediately received considerable attention in several disciplines, and in particular in the complex systems literature, although its properties are not well understood. We study the problem of finding clusterings with maximum modularity, thus providing theoretical foundations for past and present work based on this measure. More precisely, we prove the conjectured hardness of maximizing modularity both in the general case and with the restriction to cuts, and give an Integer Linear Programming formulation. This is complemented by first insights into the behavior and performance of the commonly applied greedy agglomaration approach.

Significance-Driven Graph Clustering

Modularity, the recently defined quality measure for clusterings, has attained instant popularity in the fields of social and natural sciences. We revisit the rationale behind the definition of modularity and explore the founding paradigm. This paradigm is based on the trade-off between the achieved quality and the expected quality of a clustering with respect to networks with similar intrinsic structure. We experimentally evaluate realizations of this paradigm systematically, including modularity, and describe efficient algorithms for their optimization. We confirm the feasibility of the resulting generality by a first systematic analysis of the behavior of these realizations on both artificial and on real-world data, arriving at remarkably good results of community detection.

Modularity-driven clustering of dynamic graphs

Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. As contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work we pioneer the NP-hard problem of online dynamic modularity maximization. We develop scalable dynamizations of the currently fastest and the most widespread static heuristics and engineer a heuristic dynamization of an optimal static algorithm. Our algorithms efficiently maintain a modularity-based clustering of a graph for which dynamic changes arrive as a stream. For our quickest heuristic we prove a tight bound on its number of operations. In an experimental evaluation on both a real-world dynamic network and on dynamic clustered random graphs, we show that the dynamic maintenance of a clustering of a changing graph yields higher modularity than recomputation, guarantees much smoother clustering dynamics and requires much lower runtimes. We conclude with giving recommendations for the choice of an algorithm.

Dynamic graph clustering combining modularity and smoothness

Maximizing the quality index modularity has become one of the primary methods for identifying the clustering structure within a graph. Since many contemporary networks are not static but evolve over time, traditional static approaches can be inappropriate for specific tasks. In this work, we pioneer the NP-hard problem of online dynamic modularity maximization. We develop scalable dynamizations of the currently fastest and the most widespread static heuristics and engineer a heuristic dynamization of an optimal static algorithm. Our algorithms efficiently maintain a modularity-based clustering of a graph for which dynamic changes arrive as a stream. For our quickest heuristic we prove a tight bound on its number of operations. In an experimental evaluation on both a real-world dynamic network and on dynamic clustered random graphs, we show that the dynamic maintenance of a clustering of a changing graph yields higher modularity than recomputation, guarantees much smoother clustering dynamics, and requires much lower runtimes. We conclude with giving sound recommendations for the choice of an algorithm.

Orca Reduction and ContrAction Graph Clustering

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.

Engineering Comparators for Graph Clusterings

A promising approach to compare two graph clusterings is based on using measurements for calculating the distance between them. Existing measures either use the structure of clusterings or quality-based aspects with respect to some index evaluating both clusterings. Each approach suffers from conceptional drawbacks. We introduce a new approach combining both aspects and leading to better results for comparing graph clusterings. An experimental evaluation of existing and new measures shows that the significant drawbacks of existing techniques are not only theoretical in nature but manifest frequently on different types of graphs. The evaluation also proves that the results of our new measures are highly coherent with intuition, while avoiding the former weaknesses.

Experiments on Density-Constrained Graph Clustering

Clustering a graph means identifying internally dense subgraphs that are only sparsely interconnected. Formalizations of this notion lead to measures that quantify the quality of a clustering and to algorithms that actually find clusterings. Since, most generally, corresponding optimization problems are hard, heuristic clustering algorithms are used in practice, or other approaches that are not based on an objective function. In this work, we conduct a comprehensive experimental evaluation of the qualitative behavior of greedy bottom-up heuristics driven by cut-based objectives and constrained by intracluster density, using both real-world data and artificial instances. Our study documents that a greedy strategy based on local movement is superior to one based on merging. We further reveal that the former approach generally outperforms alternative setups and reference algorithms from the literature in terms of its own objective, while a modularity-based algorithm competes surprisingly well. Finally, we exhibit which combinations of cut-based inter- and intracluster measures are suitable for identifying a hidden reference clustering in synthetic random graphs and discuss the skewness of the resulting cluster size distributions. Our results serve as a guideline to the usage of bicriterial, cut-based measures for graph clusterings.

LunarVis - analytic visualizations of large graphs

The analysis and the exploration of complex networks nowadays involves the identification of a multitude of analytic properties that have been ascertained to constitute crucial characteristics of networks. We propose a new layout paradigm for drawing large networks, with a focus on decompositional properties. The visualization is based on the general shape of an annulus and supports the immediate recognition of a large number of abstract features of the decomposition while drawing all elements. Our layouts offer remarkable readability of the decompositional connectivity and are capable of revealing subtle structural traits.

Static and Dynamic Aspects of Scientific Collaboration Networks

Collaboration networks arise when we map the connections between scientists which are formed through joint publications. These networks thus display the social structure of academia, and also allow conclusions about the structure of scientific knowledge. Using the computer science publication database DBLP, we compile relations between authors and publications as graphs and proceed with examining and quantifying collaborative relations with graph-based methods. We review standard properties of the network and rank authors and publications by centrality. Additionally, we detect communities with modularity-based clustering and compare the resulting clusters to a ground-truth based on conferences and thus topical similarity. In a second part, we are the first to combine DBLP network data with data from the Dagstuhl Seminars: We investigate whether seminars of this kind, as social and academic events designed to connect researchers, leave a visible track in the structure of the collaboration network. Our results suggest that such single events are not influential enough to change the network structure significantly. However, the network structure seems to influence a participants decision to accept or decline an invitation.