Community Detection in Bipartite Networks Using Random Walks

The community structure is a major feature of bipartite networks, which serve as a typical model for empirical networks consisting of two kinds of nodes. Over the past years, community detection has drawn a lot of attention. Numerous methods for community detection have been put forth. Nevertheless, some of them need a lot of time, which restricts their use in large networks. While several low-time complexity algorithms exist, their practical value in real-world applications is limited since they are typically non-deterministic. Typically, in bipartite networks, a unipartite projection of one part of the network is created, and then communities are detected inside that projection using methods for unipartite networks. Unipartite projections may yield incorrect or erroneous findings as they inevitably include a loss of information. In this paper, BiVoting, a two-mode and deterministic community detection method in bipartite networks, is proposed. This method is a consequence of bipartite modularity, which quantifies the strength of partitions and is based on how people vote in social elections. The proposed method’s performance was evaluated, and comparison with four common community detection methods in bipartite networks shows that for calculating the modularity score in large networks, BiVoting performs better than the best method.

Community detection is one of the primary tools to discover useful information that is hidden in complex networks. Some community detection algorithms for bipartite networks have been proposed from various viewpoints. However, the performance of these algorithms deteriorates when the community structure becomes unclear. Enhancing community structure remains a nontrivial task. In this paper, we propose a community detection algorithm, called ECD, that enhances community structure in bipartite networks. In the proposed ECD, the topology of a network is modified by reducing unnecessary edges that are connected to neighboring low-weight communities. Therefore, an ambiguous community structure is converted into a structure that is much clearer than the original structure. The experimental results on both artificial and real-world networks verify the accuracy and reliability of our algorithm. Compared with existing community detection algorithms using state-of-the-art methods, our algorithm has better performance.

Mapping network flows provides insight into the organization of networks, but even though many real networks are bipartite, no method for mapping flows takes advantage of the bipartite structure. What do we miss by discarding this information and how can we use it to understand the structure of bipartite networks better? The map equation models network flows with a random walk and exploits the information-theoretic duality between compression and finding regularities to detect communities in networks. However, it does not use the fact that random walks in bipartite networks alternate between node types, information worth 1 bit. To make some or all of this information available to the map equation, we developed a coding scheme that remembers node types at different rates. We explored the community landscape of bipartite real-world networks from no node-type information to full node-type information and found that using node types at a higher rate generally leads to deeper community hierarchies and a higher resolution. The corresponding compression of network flows exceeds the amount of extra information provided. Consequently, taking advantage of the bipartite structure increases the resolution and reveals more network regularities.

Many aspects from real life with bi-relational structure can be modeled as bipartite networks. This modeling allows the use of some standard solutions for prediction and/or recommendation of new relations between objects in such networks. In this work, we combine an existing bipartite local models method with approaches for link prediction from communities to address the link prediction problem in this type of networks. The motivation of this work stems from the importance of an application task, drug–target interaction prediction. Searching valid drug candidates for a given biological target is an essential part of modern drug development. We model the problem as link prediction in a bipartite multi-layer network, which helps to aggregate different sources of information into one single structure and as a result improves the quality of link prediction. We adapt existing community measures for link prediction to the case of bipartite multi-layer networks, propose alternative ways for exploiting communities, and show experimentally that our approach is competitive with the state-of-the-art. We also demonstrate the scalability of our approach and assess interpretability. Additional evaluations on data of a different origin than drug–target interactions demonstrate the genericness of the proposed approach.

Graph matching consists of aligning the vertices of two unlabeled graphs in order to maximize the shared structure across networks; when the graphs are unipartite, this is commonly formulated as minimizing their edge disagreements. In this paper we address the common setting in which one of the graphs to match is a bipartite network and one is unipartite. Commonly, the bipartite networks are collapsed or projected into a unipartite graph, and graph matching proceeds as in the classical setting. This potentially leads to noisy edge estimates and loss of information. We formulate the graph matching problem between a bipartite and a unipartite graph using an undirected graphical model, and introduce methods to find the alignment with this model without collapsing. We theoretically demonstrate that our methodology is consistent, and provide non-asymptotic conditions that ensure exact recovery of the matching solution. In simulations and real data examples, we show how our methods can result in a more accurate matching than the naive approach of transforming the bipartite networks into unipartite, and we demonstrate the performance gains achieved by our method in simulated and real data networks, including a co-authorship-citation network pair, and brain structural and functional data.

An evolving model of online bipartite networks

Community Detection method based on Random walk and Multi objective Evolutionary algorithm in complex networks

We study how the community structure of bipartite mutualistic networks changes in a dynamic context. First, we consider a real mutualistic network and introduce extinction events according to several scenarios. We model extinctions as node or interaction removals. For node removal, we consider random, directed and sequential extinctions; for interaction removal, we consider random extinctions. The bipartite network reorganizes showing an increase of the effective modularity and a fast decrease of the persistence of the species in the original communities with increasing number of extinction events. Second, we compare extinctions in a real mutualistic network with the growth of a bipartite network model. The modularity reaches a stationary value and nodes remain in the same community after joining the network. Our results show that perturbations and disruptive events affect the connectivity pattern of mutualistic networks at the mesoscale level. The increase of the effective modularity observed in some scenarios could provide some protection to the remaining ecosystem.

Link prediction is one of the methods of social network analysis. Bipartite networks are a type of complex network that can be used to model many natural events. In this study, a novel similarity measure for link prediction in bipartite networks is presented. Due to the fact that classical social network link prediction methods are less efficient and effective for use in bipartite network, it is necessary to use bipartite network-specific methods to solve this problem. The purpose of this study is to provide a centralized and comprehensive method based on the neighborhood structure that performs better than the existing classical methods. The proposed method consists of a combination of criteria based on the neighborhood structure. Here, the classical criteria for link prediction by modifying the bipartite network are defined. These modified criteria constitute the main component of the proposed similarity measure. In addition to low simplicity and complexity, this method has high efficiency. The simulation results show that the proposed method with a superiority of 0.5% over MetaPath, 1.32% over FriendLink, and 1.8% over Katz in thef-measure criterion shows the best performance.

Modularity and projection of bipartite networks

Community detection has realistic meaning to the research of network structure. In this paper, we propose a community detection algorithm (BSSCD algorithm) by calculating the similarity of nodes and dividing the nodes with maximum similarity into the same community. In order to accurately calculate the similarity of nodes, we define a novel similarity calculation method which combines Salton index and the improved Logistic function by analyzing the structural characteristics of two types of nodes in bipartite networks and their effects on the density of community. BSSCD algorithm does not require prior knowledge about the number of communities and the result obtained with BSSCD algorithm is very stable. Experiments on real world network datasets show that the similarity calculation method can improve accuracy of similarity calculation and BSSCD algorithm is an efficient method for community detection in bipartite networks.

Local community detection aims to obtain the local communities to which target nodes belong, by employing only partial information of the network. As a commonly used network model, bipartite applies naturally when modeling relations between two different classes of objects. There are three problems to be solved in local community detection, such as initial core node selection, expansion approach and community boundary criteria. In this work, a similarity based local community detection algorithm for bipartite networks (SLCDB) is proposed, and the algorithm can be used to detect local community structure by only using either type of nodes of a bipartite network. Experiments on real data prove that SLCDB algorithms output community structure can achieve a very high modularity which outperforms most existing local community detection methods for bipartite networks.

Detecting communities from complex networks is an important issue and has attracted attention of researchers in many fields. It is relevant to social tasks, biological inquiries, and technological problems since various networks exist in these systems. This paper proposes a new self-organizing map (SOM) based approach to community detection. By adopting a new operation and a new weight-updating scheme, a complex network can be organized into dense subgraphs according to the topological connection of each node by the SOM algorithm. Extensive numerical experiments show that the performance of the SOM algorithm is good. It can identify communities more accurately than existing methods. This method can be used to detect communities not only in undirected networks, but also in directed networks and bipartite networks.

Complex networks play a significant role in our daily lives. Due to the fact that complex networks, in reality, could suffer from manifold perturbations and network components could break down, it is, therefore, pivotal to investigate the robustness of complex networks in the face of perturbations. In the literature, enormous endeavors have been made to study network robustness. However, existing studies mainly deal with the interdependent networks, while little attention is paid to study the robustness of bipartite networks. Many networks, such as economical networks and biological networks, can be modeled as bipartite networks. It is therefore important to study the robustness of bipartite networks. Because the structures of bipartite networks differ from that of networks in common sense, existing robustness analysis methods cannot be applied to bipartite networks. With regard to this, this paper proposes a generic method based on the probabilistic theory to assess the robustness of bipartite networks under random node failures. The proposed method mathematically indicates that bipartite networks are robust to random perturbations. The experiments on random bipartite Erdos–Renyi and scale-free networks demonstrate that the theoretical results yielded by the proposed method coincide quite well with the simulation results. This paper also compares the proposed method against the well-studied method. The experiments indicate that the proposed method outperforms the comparison method.

In this paper, we propose a new algorithm for the joint clustering of two sets of statistical units N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}$$\\end{document} and M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {M}$$\\end{document} which are also equipped with an adjacency structure which is represented by a bipartite network. Our model is based on the fuzzy Partition Around Medoids, and it combines it with techniques for community detection in bipartite complex networks based on Barber modularity maximization. The goal is to produce a partition of N∪M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}\\cup \\mathcal {M}$$\\end{document} into clusters, each of which is also identified by two medoids, one in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}$$\\end{document} and one in M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {M}$$\\end{document}, which represent the typical units in the cluster for each set. Such clusters are optimized so that units in the same cluster both have similar values on their attributes and are likely to be adjacent. We test the algorithm on both simulated and real data, to show how it is able to capture a wide range of different interactions between the distribution of the attributes and the network structure.