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

The challenge of transformation

I am going to address four questions: How are we doing in England? What has worked? What has not worked? What is next?Education

Vot Long Pati Ia! (Your vote, our party)

Review of the film "Vot Long Pati Ia!" The film is made by Wan Smolbag Theatre in Vanuatu and is a fascinating dramatization of political and developmental dilemmas in the South Pacific

Is the European R&D network homogeneous? spatial interaction modeling of network communities determined using graph theoretic methods

Interactions between firms, universities, and research organizations are crucial for successful innovation in the modern knowledge-based economy. Systems of such interactions constitute R&D networks. R&D networks may be meaningful segmented using recent methods for identifying communities, subnetworks whose members are more tightly linked to one another than to other members of the network. In this paper, we identify such communities in the European R&D network using data on joint research projects funded by the fifth European Framework Programme. We characterize the identified communities according to their thematic orientation and spatial structure. By means of a Poisson spatial interaction model, we estimate the impact of various separation factors – such as geographical distance – on the variation of cross-region collaboration activities in a given community. The European coverage is achieved by using data on 255 NUTS-2 regions of the 25 pre-2007 EU member-states, as well as Norway and Switzerland. The results demonstrate that European R&D networks are not homogeneous, instead showing relevant community substructures with distinct thematic and spatial properties.

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