Network community-detection enhancement by proper weighting

Modularity in Biological Networks

Network modeling, from the ecological to the molecular scale has become an essential tool for studying the structure, dynamics and complex behavior of living systems. Graph representations of the relationships between biological components open up a wide variety of methods for discovering the mechanistic and functional properties of biological systems. Many biological networks are organized into a modular structure, so methods to discover such modules are essential if we are to understand the biological system as a whole. However, most of the methods used in biology to this end, have a limited applicability, as they are very specific to the system they were developed for. Conversely, from the statistical physics and network science perspective, graph modularity has been theoretically studied and several methods of a very general nature have been developed. It is our perspective that in particular for the modularity detection problem, biology and theoretical physics/network science are less connected than they should. The central goal of this review is to provide the necessary background and present the most applicable and pertinent methods for community detection in a way that motivates their further usage in biological research.

Co-Association Matrix-Based Multi-Layer Fusion for Community Detection in Attributed Networks

Community detection is a challenging task in attributed networks, due to the data inconsistency between network topological structure and node attributes. The problem of how to effectively and robustly fuse multi-source heterogeneous data plays an important role in community detection algorithms. Although some algorithms taking both topological structure and node attributes into account have been proposed in recent years, the fusion strategy is simple and usually adopts the linear combination method. As a consequence of this, the detected community structure is vulnerable to small variations of the input data. In order to overcome this challenge, we develop a novel two-layer representation to capture the latent knowledge from both topological structure and node attributes in attributed networks. Then, we propose a weighted co-association matrix-based fusion algorithm (WCMFA) to detect the inherent community structure in attributed networks by using multi-layer fusion strategies. It extends the community detection method from a single-view to a multi-view style, which is consistent with the thinking model of human beings. Experiments show that our method is superior to the state-of-the-art community detection algorithms for attributed networks.

Micro-blog user community discovery using generalized SimRank edge weighting method

Community discovery is one of the most popular issues in analyzing and understanding a network. Previous research suggests that the discovery can be enhanced by assigning weights to the edges of the network. This paper proposes a novel edge weighting method, which balances both local and global weighting based on the idea of shared neighbor ranging between users and the interpersonal significance of the social network community. We assume that users belonging to the same community have similar relationship network structures. By controlling the measure of "neighborhood", this method can adequately adapt to real-world networks. Therefore, the famous similarity calculation method-SimRank-can be regarded as a special case of our method. According to the practical significance of social networks, we propose a new evaluation method that uses the communication rate to measure its divided demerit to better express users' interaction relations than the ordinary modularity Q. Furthermore, the fast Newman algorithm is extended to weighted networks. In addition, we use four real networks in the largest Chinese micro-blog website Sina. The results of experiments demonstrate that the proposed method easily meets the balancing requirements and is more robust to different kinds of networks. The experimental results also indicate that the proposed algorithm outperforms several conventional weighting methods.

Network clustering and community detection using modulus of families of loops

We study the structure of loops in networks using the notion of modulus of loop families. We introduce an alternate measure of network clustering by quantifying the richness of families of (simple) loops. Modulus tries to minimize the expected overlap among loops by spreading the expected link usage optimally. We propose weighting networks using these expected link usages to improve classical community detection algorithms. We show that the proposed method enhances the performance of certain algorithms, such as spectral partitioning and modularity maximization heuristics, on standard benchmarks.

The network architecture of the Saccharomyces cerevisiae genome

We propose a network-based approach for surmising the spatial organization of genomes from high-throughput interaction data. Our strategy is based on methods for inferring architectural features of networks. Specifically, we employ a community detection algorithm to partition networks of genomic interactions. These community partitions represent an intuitive interpretation of genomic organization from interaction data. Furthermore, they are able to recapitulate known aspects of the spatial organization of the Saccharomyces cerevisiae genome, such as the rosette conformation of the genome, the clustering of centromeres, as well as tRNAs, and telomeres. We also demonstrate that simple architectural features of genomic interaction networks, such as cliques, can give meaningful insight into the functional role of the spatial organization of the genome. We show that there is a correlation between inter-chromosomal clique size and replication timing, as well as cohesin enrichment. Together, our network-based approach represents an effective and intuitive framework for interpreting high-throughput genomic interaction data. Importantly, there is a great potential for this strategy, given the rich literature and extensive set of existing tools in the field of network analysis.

Normalized modularity optimization method for community identification with degree adjustment

As a fundamental problem in network study, community identification has attracted much attention from different fields. Representing a seminal work in this area, the modularity optimization method has been widely applied and studied. However, this method has issues in resolution limit and extreme degeneracy and may not perform well for networks with unbalanced structures. Although several methods have been proposed to overcome these limitations, they are all based on the original idea of defining modularity through comparing the total number of edges within the putative communities in the observed network with that in an equivalent randomly generated network. In this paper, we show that this modularity definition is not suitable to analyze some networks such as those with unbalanced structures. Instead, we propose to define modularity through the average degree within the communities and formulate modularity as comparing the sum of average degree within communities of the observed network to that of an equivalent randomly generated network. In addition, we also propose a degree-adjusted approach for further improvement when there are unbalanced structures. We analyze the theoretical properties of our degree adjusted method. Numerical experiments for both artificial networks and real networks demonstrate that average degree plays an important role in network community identification, and our proposed methods have better performance than existing ones.

Community identification in networks with unbalanced structure

Community (module) structure is a common and important property of many types of networks, such as social networks and biological networks. Several classes of algorithms have been proposed for community structure detection and identification, including clustering techniques, modularity optimization, and other methods. Among these methods, the modularity optimization method has attracted a great deal of attention and much related research has been published. However, the existing modularity optimization method does not perform well in the presence of unbalanced community structures. In this paper, we introduce a metric to characterize the community structure better than other metrics in this situation, and we propose a method to infer the number of communities, which may solve the resolution limit problem. We then develop an algorithm for community structure identification based on eigendecompositions, and we give both simulated and real data examples to illustrate the better performance of our approach.

Finding communities in weighted networks through synchronization

Community detection in weighted networks is an important challenge. In this paper, we introduce a local weight ratio scheme for identifying the community structures of weighted networks within the context of the Kuramoto model by taking into account weights of links. The proposed scheme takes full advantage of the information of the link density among vertices and the closeness of relations between each vertex and its neighbors. By means of this scheme, we explore the connection between community structures and dynamic time scales of synchronization. Moreover, we can also unravel the hierarchical structures of weighted networks with a well-defined connectivity pattern by the synchronization process. The performance of the proposed method is evaluated on both computer-generated benchmark graphs and real-world networks.

An iterative network partition algorithm for accurate identification of dense network modules

A key step in network analysis is to partition a complex network into dense modules. Currently, modularity is one of the most popular benefit functions used to partition network modules. However, recent studies suggested that it has an inherent limitation in detecting dense network modules. In this study, we observed that despite the limitation, modularity has the advantage of preserving the primary network structure of the undetected modules. Thus, we have developed a simple iterative Network Partition (iNP) algorithm to partition a network. The iNP algorithm provides a general framework in which any modularity-based algorithm can be implemented in the network partition step. Here, we tested iNP with three modularity-based algorithms: multi-step greedy (MSG), spectral clustering and Qcut. Compared with the original three methods, iNP achieved a significant improvement in the quality of network partition in a benchmark study with simulated networks, identified more modules with significantly better enrichment of functionally related genes in both yeast protein complex network and breast cancer gene co-expression network, and discovered more cancer-specific modules in the cancer gene co-expression network. As such, iNP should have a broad application as a general method to assist in the analysis of biological networks.