Biclique communities

We present a novel method for detecting communities in bipartite networks. Based on an extension of the $k$-clique community detection algorithm, we demonstrate how modular structure in bipartite networks presents itself as overlapping bicliques. If bipartite information is available, the bi-clique community detection algorithm retains all of the advantages of the $k$-clique algorithm, but avoids discarding important structural information when performing a one-mode projection of the network. Further, the bi-clique community detection algorithm provides a new level of flexibility by incorporating independent clique thresholds for each of the non-overlapping node sets in the bipartite network.Comment: 10 pages, 6 figure

Detecting and generating overlapping nested communities

Nestedness has been observed in a variety of networks but has been primarily viewed in the context of bipartite networks. Numerous metrics quantify nestedness and some clustering methods identify fully nested parts of graphs, but all with similar limitations. Clustering approaches also fail to uncover the overlap between fully nested subgraphs, as they assign vertices to a single group only. In this paper, we look at the nestedness of a network through an auxiliary graph, in which a directed edge represents a nested relationship between the two corresponding vertices of the network. We present an algorithm that recovers this so-called community graph, and finds the overlapping fully nested subgraphs of a network. We also introduce an algorithm for generating graphs with such nested structure, given by a community graph. This algorithm can be used to test a nested community detection algorithm of this kind, and potentially to evaluate different metrics of nestedness as well. Finally, we evaluate our nested community detection algorithm on a large variety of networks, including bipartite and non-bipartite ones, too. We derive a new metric from the community graph to quantify the nestedness of both bipartite and non-bipartite networks

Detecting Cohesive and 2-mode Communities in Directed and Undirected Networks

Networks are a general language for representing relational information among objects. An effective way to model, reason about, and summarize networks, is to discover sets of nodes with common connectivity patterns. Such sets are commonly referred to as network communities. Research on network community detection has predominantly focused on identifying communities of densely connected nodes in undirected networks. In this paper we develop a novel overlapping community detection method that scales to networks of millions of nodes and edges and advances research along two dimensions: the connectivity structure of communities, and the use of edge directedness for community detection. First, we extend traditional definitions of network communities by building on the observation that nodes can be densely interlinked in two different ways: In cohesive communities nodes link to each other, while in 2-mode communities nodes link in a bipartite fashion, where links predominate between the two partitions rather than inside them. Our method successfully detects both 2-mode as well as cohesive communities, that may also overlap or be hierarchically nested. Second, while most existing community detection methods treat directed edges as though they were undirected, our method accounts for edge directions and is able to identify novel and meaningful community structures in both directed and undirected networks, using data from social, biological, and ecological domains.Comment: Published in the proceedings of WSDM '1

A Unified Community Detection, Visualization and Analysis method

Community detection in social graphs has attracted researchers' interest for a long time. With the widespread of social networks on the Internet it has recently become an important research domain. Most contributions focus upon the definition of algorithms for optimizing the so-called modularity function. In the first place interest was limited to unipartite graph inputs and partitioned community outputs. Recently bipartite graphs, directed graphs and overlapping communities have been investigated. Few contributions embrace at the same time the three types of nodes. In this paper we present a method which unifies commmunity detection for the three types of nodes and at the same time merges partitionned and overlapping communities. Moreover results are visualized in such a way that they can be analyzed and semantically interpreted. For validation we experiment this method on well known simple benchmarks. It is then applied to real data in three cases. In two examples of photos sets with tagged people we reveal social networks. A second type of application is of particularly interest. After applying our method to Human Brain Tractography Data provided by a team of neurologists, we produce clusters of white fibers in accordance with other well known clustering methods. Moreover our approach for visualizing overlapping clusters allows better understanding of the results by the neurologist team. These last results open up the possibility of applying community detection methods in other domains such as data analysis with original enhanced performances.Comment: Submitted to Advances in Complex System

Finding maximal bicliques in bipartite networks using node similarity

In real world complex networks, communities are usually both overlapping and hierarchical. A very important class of complex networks is the bipartite networks. Maximal bicliques are the strongest possible structural communities within them. Here we consider overlapping communities in bipartite networks and propose a method that detects an order-limited number of overlapping maximal bicliques covering the network. We formalise a measure of relative community strength by which communities can be categorised, compared and ranked. There are very few real bipartite datasets for which any external ground truth about overlapping communities is known. Here we test three such datasets. We categorise and rank the maximal biclique communities found by our algorithm according to our measure of strength. Deeper analysis of these bicliques shows they accord with ground truth and give useful additional insight. Based on this we suggest our algorithm can find true communities at the first level of a hierarchy. We add a heuristic merging stage to the maximal biclique algorithm to produce a second level hierarchy with fewer communities and obtain positive results when compared with other overlapping community detection algorithms for bipartite networks

Complex information networks – detecting community structure in bipartite networks

The last decade has witnessed great expansion in research and study of complex networks. A complex network is a large-scale network that reflects the interactions between objects or components of complicated systems. These components, known as clusters, communities or modules, perform together in order to provide one or more functions of the system. A vast number of systems, from the brain to ecosystems, power grids and the Internet, criminal relationships and financial transactions, can all be described as large complex networks. For most complex networks, the complexity arises from the fact that the structure is highly irregular, complex and dynamically evolving in time; and that the observed patterns of interactions highly influence the behaviour of the entire system. One of the topological properties that can expose the hierarchical structure of complex networks is community structure. Community detection is a common problem in complex networks that consists in general of finding groups of densely connected nodes with few connections to nodes outside of a group. The lack of consensus on a definition for a community leads to extensive studies on community structure of complex networks in order to provide improved community detection methods. Community structure is a common and important topological characteristic of many real world complex networks. In particular, identifying communities in bipartite networks is an important task in many scientific domains. In a bipartite network, the node set consists of two disjoint sets of nodes, primary set (P) and secondary set (S), such that links between nodes may occur only if the nodes belong to different sets. There are really two approaches to identifying clusters in a bipartite network: the first, and more common, is when our real interest is in community structure within the primary node set P; and the second is when our real interest is in bipartite communities within the whole network. Thus, in this research we investigate and study the state-of-the-art of community detection algorithms, in particular, those to identify the communities in bipartite networks in order to provide us with a more complete understanding of the relationship between communities. The practical aim is to derive a coarse-grain description of the network topology that will aid understanding of its hierarchical structure. The research of the thesis consists of four main phases. First, one of the best algorithms for community detection in classical networks, Infomap, has not been adapted to the big and important class of bipartite networks. This research gap is one focus of the thesis. We integrate the weighted projection method for bipartite networks based on common neighbors similarity into Infomap, to acquire a weighted one mode network that can be clustered by this random walks technique. We apply this method to a number of real world bipartite networks, to detect significant community structure. We measure the performance of our approach based on the ground truth. This requires deep knowledge of the formation of relations within and between clusters in these real world networks. Although such investigation is excessively time consuming, and impractical or impossible in large networks, the result is much more accurate and more meaningful and gives us confidence that this method can be usefully applied to large networks where ground truth is not known. Second, several possible edge additions are conducted to test how random walks based algorithm, Infomap, performs when the minimal modification is made to convert a bipartite network to a nearly bipartite (but unipartite) network. The experiments on small bipartite networks obtain encouraging results. Third, we shift focus from community detection based on random walks to community detection based on the strongest communities possible in a bipartite network, which are bicliques. We develop a novel algorithm to identify overlapping communities at the base level of hierarchy in bipartite networks. We combine existing techniques (bicliques, cliques, structural equivalence) into a novel method to solve this new research problem. We classify the output communities into 5 categories based on community strength. From this base level, we apply the Jaccard index as a threshold in order to reduce the redundancy of overlapping communities, to obtain higher levels of the hierarchy. We compare results from our overlapping approach with other concurrent approaches not only directly to the ground truth, but also using a widely accepted scale for evaluating the quality of partitions, Normalized Mutual Information (NMI). In the last phase of the thesis, a large financial bipartite network collected during 6 months fieldwork is analysed and tested in order to reveal its hierarchical structure. We apply all methods presented in Chapter 3, Chapter 4 and Chapter 5. The main contribution of this thesis is an improved method to detect the hierarchical and overlapping community structure in bipartite complex networks based on structural equivalence of nodes. More generally, it aims to derive a coarse-grain depiction of real large-scale networks through structural properties of their identified communities as well as their performance with respect to the known ground truth

Community detection for networks with unipartite and bipartite structure

Finding community structures in networks is important in network science, technology, and applications. To date, most algorithms that aim to find community structures only focus either on unipartite or bipartite networks. A unipartite network consists of one set of nodes and a bipartite network consists of two nonoverlapping sets of nodes with only links joining the nodes in different sets. However, a third type of network exists, defined here as the mixture network. Just like a bipartite network, a mixture network also consists of two sets of nodes, but some nodes may simultaneously belong to two sets, which breaks the nonoverlapping restriction of a bipartite network. The mixture network can be considered as a general case, with unipartite and bipartite networks viewed as its limiting cases. A mixture network can represent not only all the unipartite and bipartite networks, but also a wide range of real-world networks that cannot be properly represented as either unipartite or bipartite networks in fields such as biology and social science. Based on this observation, we first propose a probabilistic model that can find modules in unipartite, bipartite, and mixture networks in a unified framework based on the link community model for a unipartite undirected network [B Ball et al (2011 Phys. Rev. E 84 036103)]. We test our algorithm on synthetic networks (both overlapping and nonoverlapping communities) and apply it to two real-world networks: a southern women bipartite network and a human transcriptional regulatory mixture network. The results suggest that our model performs well for all three types of networks, is competitive with other algorithms for unipartite or bipartite networks, and is applicable to real-world networks.Comment: 27 pages, 8 figures. (http://iopscience.iop.org/1367-2630/16/9/093001

Overlapping Community Detection Optimization and Nash Equilibrium

Community detection using both graphs and social networks is the focus of many algorithms. Recent methods aimed at optimizing the so-called modularity function proceed by maximizing relations within communities while minimizing inter-community relations. However, given the NP-completeness of the problem, these algorithms are heuristics that do not guarantee an optimum. In this paper, we introduce a new algorithm along with a function that takes an approximate solution and modifies it in order to reach an optimum. This reassignment function is considered a 'potential function' and becomes a necessary condition to asserting that the computed optimum is indeed a Nash Equilibrium. We also use this function to simultaneously show partitioning and overlapping communities, two detection and visualization modes of great value in revealing interesting features of a social network. Our approach is successfully illustrated through several experiments on either real unipartite, multipartite or directed graphs of medium and large-sized datasets.Comment: Submitted to KD