Detecting hierarchical and overlapping network communities using locally optimal modularity changes

Agglomerative clustering is a well established strategy for identifying communities in networks. Communities are successively merged into larger communities, coarsening a network of actors into a more manageable network of communities. The order in which merges should occur is not in general clear, necessitating heuristics for selecting pairs of communities to merge. We describe a hierarchical clustering algorithm based on a local optimality property. For each edge in the network, we associate the modularity change for merging the communities it links. For each community vertex, we call the preferred edge that edge for which the modularity change is maximal. When an edge is preferred by both vertices that it links, it appears to be the optimal choice from the local viewpoint. We use the locally optimal edges to define the algorithm: simultaneously merge all pairs of communities that are connected by locally optimal edges that would increase the modularity, redetermining the locally optimal edges after each step and continuing so long as the modularity can be further increased. We apply the algorithm to model and empirical networks, demonstrating that it can efficiently produce high-quality community solutions. We relate the performance and implementation details to the structure of the resulting community hierarchies. We additionally consider a complementary local clustering algorithm, describing how to identify overlapping communities based on the local optimality condition.Comment: 10 pages; 4 tables, 3 figure

NetzCope: A Tool for Displaying and Analyzing Complex Networks

Networks are a natural and popular mechanism for the representation and investigation of a broad class of systems. But extracting information from a network can present significant challenges. We present NetzCope, a software application for the display and analysis of networks. Its key features include the visualization of networks in two or three dimensions, the organization of vertices to reveal structural similarity, and the detection and visualization of network communities by modularity maximization.Comment: 16 pages, Proceedings of ICQBIC2010; minor improvements to wording in v

The structure of R&D collaboration networks in the European Framework Programmes

Using a large and novel data source, we study the structure of R&D collaboration net-works in the first five EU Framework Programmes (FPs). The networks display proper-ties typical for complex networks, including scale-free degree distributions and the small-world property. Structural features are common across FPs, indicating similar network formation mechanisms despite changes in governance rules. Several findings point towards the existence of a stable core of interlinked actors since the early FPs with integration increasing over time. This core consists mainly of universities and research organisations. We observe assortative mixing by degree of projects, but not by degree of organisations. Unexpectedly, we find only weak association between central projects and project size, suggesting that different types of projects attract different groups of actors. In particular, large projects appear to have included few of the pivotal actors in the networks studied. Central projects only partially mirror funding priorities, indicating field-specific differences in network structures. The paper concludes with an agenda for future research.R&D collaboration, EU Framework Programmes, Complex Networks, Small World Effect, Centrality Measures, European Research Area

R&D collaboration networks in the European FrameworkProgrammes: Data processing, network construction and selected results

We describe the construction of a large and novel data set on R&D collaboration networks in the first five EU Framework Programmes (FPs), examine key features and provide economic interpretations for our findings. The data set is based on publicly available raw data that pre-sents numerous challenges. We critically examine the different problems and detail how we have dealt with them. We describe how we construct networks from the processed data. The resulting networks display properties typical for large complex networks, including scale-free degree distributions and the small-world property. The former indicates the presence of net-work hubs, which we identify. Theoretical work shows the latter to be beneficial for knowl-edge creation and diffusion. Structural features are remarkably similar across FPs, indicating similar network formation mechanisms despite changes in governance rules. Several findings point towards the existence of a stable core of interlinked actors since the early FPs with inte-gration increasing over time. This core consists mainly of universities and research organisa-tions. The paper concludes with an agenda for future research.R&D collaboration, EU Framework Programmes, complex networks, small world effect, knowledge creation, knowledge diffusion, European Research Area

The Community Structure of R&D Cooperation in Europe. Evidence from a social network perspective

The focus of this paper is on pre-competitive R&D cooperation across Europe, as captured by R&D joint ventures funded by the European Commission in the time period 1998-2002, within the 5th Framework Program. The cooperations in this Framework Program give rise to a bipartite network with 72,745 network edges between 25,839 actors (representing organizations that include firms, universities, research organizations and public agencies) and 9,490 R&D projects. With this construction, participating actors are linked only through joint projects. In this paper we describe the community identification problem based on the concept of modularity, and use the recently introduced label-propagation algorithm to identify communities in the network, and differentiate the identified communities by developing community-specific profiles using social network analysis and geographic visualization techniques. We expect the results to enrich our picture of the European Research Area by providing new insights into the global and local structures of R&D cooperation across Europe