A framework for community detection in heterogeneous multi-relational networks

There has been a surge of interest in community detection in homogeneous single-relational networks which contain only one type of nodes and edges. However, many real-world systems are naturally described as heterogeneous multi-relational networks which contain multiple types of nodes and edges. In this paper, we propose a new method for detecting communities in such networks. Our method is based on optimizing the composite modularity, which is a new modularity proposed for evaluating partitions of a heterogeneous multi-relational network into communities. Our method is parameter-free, scalable, and suitable for various networks with general structure. We demonstrate that it outperforms the state-of-the-art techniques in detecting pre-planted communities in synthetic networks. Applied to a real-world Digg network, it successfully detects meaningful communities.Comment: 27 pages, 10 figure

Fluctuations between high- and low-modularity topology in time-resolved functional connectivity

Modularity is an important topological attribute for functional brain networks. Recent studies have reported that modularity of functional networks varies not only across individuals being related to demographics and cognitive performance, but also within individuals co-occurring with fluctuations in network properties of functional connectivity, estimated over short time intervals. However, characteristics of these time-resolved functional networks during periods of high and low modularity have remained largely unexplored. In this study we investigate spatiotemporal properties of time-resolved networks in the high and low modularity periods during rest, with a particular focus on their spatial connectivity patterns, temporal homogeneity and test-retest reliability. We show that spatial connectivity patterns of time-resolved networks in the high and low modularity periods are represented by increased and decreased dissociation of the default mode network module from task-positive network modules, respectively. We also find that the instances of time-resolved functional connectivity sampled from within the high (low) modularity period are relatively homogeneous (heterogeneous) over time, indicating that during the low modularity period the default mode network interacts with other networks in a variable manner. We confirmed that the occurrence of the high and low modularity periods varies across individuals with moderate inter-session test-retest reliability and that it is correlated with previously-reported individual differences in the modularity of functional connectivity estimated over longer timescales. Our findings illustrate how time-resolved functional networks are spatiotemporally organized during periods of high and low modularity, allowing one to trace individual differences in long-timescale modularity to the variable occurrence of network configurations at shorter timescales.Comment: Reorganized the paper; to appear in NeuroImage; arXiv abstract shortened to fit within character limit

Structure of Heterogeneous Networks

Heterogeneous networks play a key role in the evolution of communities and the decisions individuals make. These networks link different types of entities, for example, people and the events they attend. Network analysis algorithms usually project such networks unto simple graphs composed of entities of a single type. In the process, they conflate relations between entities of different types and loose important structural information. We develop a mathematical framework that can be used to compactly represent and analyze heterogeneous networks that combine multiple entity and link types. We generalize Bonacich centrality, which measures connectivity between nodes by the number of paths between them, to heterogeneous networks and use this measure to study network structure. Specifically, we extend the popular modularity-maximization method for community detection to use this centrality metric. We also rank nodes based on their connectivity to other nodes. One advantage of this centrality metric is that it has a tunable parameter we can use to set the length scale of interactions. By studying how rankings change with this parameter allows us to identify important nodes in the network. We apply the proposed method to analyze the structure of several heterogeneous networks. We show that exploiting additional sources of evidence corresponding to links between, as well as among, different entity types yields new insights into network structure

Formation of Modularity in a Model of Evolving Networks

Modularity structures are common in various social and biological networks. However, its dynamical origin remains an open question. In this work, we set up a dynamical model describing the evolution of a social network. Based on the observations of real social networks, we introduced a link-creating/deleting strategy according to the local dynamics in the model. Thus the coevolution of dynamics and topology naturally determines the network properties. It is found that for a small coupling strength, the networked system cannot reach any synchronization and the network topology is homogeneous. Interestingly, when the coupling strength is large enough, the networked system spontaneously forms communities with different dynamical states. Meanwhile, the network topology becomes heterogeneous with modular structures. It is further shown that in a certain parameter regime, both the degree and the community size in the formed network follow a power-law distribution, and the networks are found to be assortative. These results are consistent with the characteristics of many empirical networks, and are helpful to understand the mechanism of formation of modularity in complex networks.Comment: 6 pages, 4 figur

Identifying "communities" within energy landscapes

Potential energy landscapes can be represented as a network of minima linked by transition states. The community structure of such networks has been obtained for a series of small Lennard-Jones clusters. This community structure is compared to the concept of funnels in the potential energy landscape. Two existing algorithms have been used to find community structure, one involving removing edges with high betweenness, the other involving optimization of the modularity. The definition of the modularity has been refined, making it more appropriate for networks such as these where multiple edges and self-connections are not included. The optimization algorithm has also been improved, using Monte Carlo methods with simulated annealing and basin hopping, both often used successfully in other optimization problems. In addition to the small clusters, two examples with known heterogeneous landscapes, LJ_13 with one labelled atom and LJ_38, were studied with this approach. The network methods found communities that are comparable to those expected from landscape analyses. This is particularly interesting since the network model does not take any barrier heights or energies of minima into account. For comparison, the network associated with a two-dimensional hexagonal lattice is also studied and is found to have high modularity, thus raising some questions about the interpretation of the community structure associated with such partitions.Comment: 13 pages, 11 figure

Modularity-based credible prediction of disease genes and detection of disease subtypes on the phenotype-gene heterogeneous network

<p>Abstract</p> <p>Background</p> <p>Protein-protein interaction networks and phenotype similarity information have been synthesized together to discover novel disease-causing genes. Genetic or phenotypic similarities are manifested as certain modularity properties in a phenotype-gene heterogeneous network consisting of the phenotype-phenotype similarity network, protein-protein interaction network and gene-disease association network. However, the quantitative analysis of modularity in the heterogeneous network and its influence on disease-gene discovery are still unaddressed. Furthermore, the genetic correspondence of the disease subtypes can be identified by marking the genes and phenotypes in the phenotype-gene network. We present a novel network inference method to measure the network modularity, and in particular to suggest the subtypes of diseases based on the heterogeneous network.</p> <p>Results</p> <p>Based on a measure which is introduced to evaluate the closeness between two nodes in the phenotype-gene heterogeneous network, we developed a Hitting-Time-based method, CIPHER-HIT, for assessing the modularity of disease gene predictions and credibly prioritizing disease-causing genes, and then identifying the genetic modules corresponding to potential subtypes of the queried phenotype. The CIPHER-HIT is free to rely on any preset parameters. We found that when taking into account the modularity levels, the CIPHER-HIT method can significantly improve the performance of disease gene predictions, which demonstrates modularity is one of the key features for credible inference of disease genes on the phenotype-gene heterogeneous network. By applying the CIPHER-HIT to the subtype analysis of Breast cancer, we found that the prioritized genes can be divided into two sub-modules, one contains the members of the Fanconi anemia gene family, and the other contains a reported protein complex MRE11/RAD50/NBN.</p> <p>Conclusions</p> <p>The phenotype-gene heterogeneous network contains abundant information for not only disease genes discovery but also disease subtypes detection. The CIPHER-HIT method presented here is effective for network inference, particularly on credible prediction of disease genes and the subtype analysis of diseases, for example Breast cancer. This method provides a promising way to analyze heterogeneous biological networks, both globally and locally.</p