Distribution characteristics of weighted bipartite evolving networks

Bipartite networks that characterize complex relationships among data arise in various domains. The existing bipartite network models are mainly based on a type of relationship between objects, and cannot effectively describe multiple relationships in the real world. In this paper, we propose a multi-relationship bipartite network (MBN) model, which can describe multiple relationships between two types of objects, and realizes simple weighted bipartite network reconstruction. Our model contains three major modules, namely multi-relationship bipartite network modeling (MBNM), multi-relationship aggregation module (MAM) and network reconstruction module (NRM). In MBNM, a multi-relationship bipartite network is proposed to describe multiple relationships between two types of objects. In the MAM, considering that different relationships have different information for the model, we introduce a novel relationship-level attention mechanism, and the aggregation of multiple relationships is carried out through the importance of each relationship. Based on the learning framework, the NRM can learn the potential representations of nodes after multi-relationship aggregation, and design a nonlinear fusion mechanism to reconstruct weighted bipartite network. We conducted extensive experiments on three real-world datasets and the results show that multi-relationship aggregation can effectively improve the performance of the model. In addition, experiments also show that our model can outperform existing competitive baseline method.

On the degree distribution of projected networks mapped from bipartite networks

This paper focuses on the synchronization for the delayed bipartite networks with non-delay and delay couplings. Different from single networks, the nodes of bipartite networks can be divided into two disjoint nonempty sets according to their properties or dynamics characteristics, and the nodes in different sets can be connected by edges while the nodes in the same set cannot be connected. In this bipartite network model, the node and coupling delays are simultaneously considered, and both the non-delay and delay coupling matrices are undirected and weighed. Furthermore, the intermittent control method used in this paper can be aperiodic while in most previous works are periodic. Based on the Lyapunov function method, block multiplication of matrices and other mathematical techniques, several synchronization protocols are rigorously induced. Finally, the proposed control method is evaluated by utilizing numerical simulation.

We describe a class of new algorithms to construct bipartite networks that preserves a prescribed degree and joint-degree (degree-degree) distribution of the nodes. Bipartite networks are graphs that can represent real-world interactions between two disjoint sets, such as actor-movie networks, author-article networks, co-occurrence networks, and heterosexual partnership networks. Often there is a strong correlation between the degree of a node and the degrees of the neighbors of that node that must be preserved when generating a network that reflects the structure of the underling system. Our bipartite 2K (B2K) algorithms generate an ensemble of networks that preserve prescribed degree sequences for the two disjoint set of nodes in the bipartite network, and the joint-degree distribution that is the distribution of the degrees of all neighbors of nodes with the same degree. We illustrate the effectiveness of the algorithms on a romance network using the NetworkX software environment to compare other properties of a target network that are not directly enforced by the B2K algorithms. We observe that when average degree of nodes is low, as is the case for romance and heterosexual partnership networks, then the B2K networks tend to preserve additional properties, such as the cluster coefficients, than algorithms that do not preserve the joint-degree distribution of the original network.

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.

A fundamental aspect of network analysis involves pinpointing nodes that hold significant positions within the network. Graph theory has emerged as a powerful mathematical tool for this purpose, and there exist numerous graph-theoretic parameters for analyzing the stability of the system. Within this framework, various graph-theoretic parameters contribute to network analysis. One such parameter used in network analysis is the so-called closeness, which serves as a structural measure to assess the efficiency of a node’s ability to interact with other nodes in the network. Mathematically, it measures the reciprocal of the sum of the shortest distances from a node to all other nodes in the network. A bipartite network is a particular type of network in which the nodes can be divided into two disjoint sets such that no two nodes within the same set are adjacent. This paper mainly studies the problem of determining the network that maximize the closeness within bipartite networks. To be more specific, we identify those networks that maximize the closeness over bipartite networks with a fixed number of nodes and one of the fixed parameters: connectivity, dissociation number, cut edges, and diameter.

Social network analysis has typically concerned analysis of one type of tie connecting nodes of the same type. It has however been recognised that people are connected through multiple types of ties and that people in addition are affiliated with multiple types of non-people nodes. Exponential random graph models (ERGM) is a family of statistical models for social networks that at this point allows for a number of different types of network data, including one-mode networks, bipartite networks, multiplex data, as well as multilevel network data. Multilevel networks have been proposed as a joint representation of associations between multiple types of entities or nodes, such as people and organization, where two types of nodes gives rise to three distinct types of ties. The typical roster data collection method may be impractical or infeasible when the node sets are hard to detect or define or because of the cognitive demands on respondents. Multilevel multilayered networks allow us to consider a multitude of different sources of data and to sample on different types of nodes and relations. We consider modelling multilevel multilayered networks using exponential random graph models and extend a recently developed Bayesian data-augmentation scheme to allow for partially missing data. We illustrate the proposed inference procedures for the case of multilevel snowball sampling and sampling with error based on the Noordin Top network.

This paper aims at targeting some relevant issues for clustering tennis players and tournaments: (i) it considers players, tournaments and the relation between them; (ii) the relation is taken into account in the fuzzy clustering model based on the Partitioning Around Medoids (PAM) algorithm through spatial constraints; (iii) the attributes of the players and of the tournaments are of different nature, qualitative and quantitative. The proposal is novel for the methodology used, a spatial Fuzzy clustering model for players and for tournaments (based on related attributes), where the spatial penalty term in each clustering model depends on the relation between players and tournaments described in the adjacency matrix. The proposed model is compared with a bipartite players-tournament complex network model (the Degree-Corrected Stochastic Blockmodel) that considers only the relation between players and tournaments, described in the adjacency matrix, to obtain communities on each side of the bipartite network. An application on data taken from the ATP official website with regards to the draws of the tournaments, and from the sport statistics website Wheelo ratings for the performance data of players and tournaments, shows the performances of the proposed clustering model.

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.

As economic entities become increasingly interconnected, a shock in a financial network can provoke significant cascading failures throughout the system. To study the systemic risk of financial systems, we create a bi-partite banking network model composed of banks and bank assets and propose a cascading failure model to describe the risk propagation process during crises. We empirically test the model with 2007 US commercial banks balance sheet data and compare the model prediction of the failed banks with the real failed banks after 2007. We find that our model efficiently identifies a significant portion of the actual failed banks reported by Federal Deposit Insurance Corporation. The results suggest that this model could be useful for systemic risk stress testing for financial systems. The model also identifies that commercial rather than residential real estate assets are major culprits for the failure of over 350 US commercial banks during 2008–2011.

Modularity and projection of bipartite networks

Bipartite graphs, representing two-mode networks, arise in many research fields. These networks have two disjoint node sets representing distinct entity types, for example persons and groups, with edges representing associations between the two entity types. In bipartite graphs, the smallest possible cycle is a cycle of length four, and hence four-cycles are the smallest structure to model closure in such networks. Exponential-family random graph models (ERGMs) are a widely used model for social, and other, networks, including specifically bipartite networks. Existing ERGM terms to model four-cycles in bipartite networks, however, are relatively rarely used. In this work we demonstrate some problems with these existing terms to model four-cycles, and define new ERGM terms to help overcome these problems. The position of the new terms in the ERGM dependence hierarchy, and their interpretation, is discussed. The new terms are demonstrated in simulation experiments, and their application illustrated on a canonical example of an empirical two-mode network.

Bipartite network with rewiring dynamics exists in many real-world networks. Various models based on the mean-field approximation are successfully proposed for the degree distribution of rewiring dynamics in the bipartite network. However, there are implicit or even obvious differences among these models, despite that they are utilized for modeling the same rewiring problem. How the differences among these models arise and how the differences influence the solution of the degree distribution remain unresolved. Firstly, the models for a bipartite network with rewiring dynamics are categorized into three versions, which are named as a two steps version model (TSV model), a one step version-I model (OSV-I model), and a one step version-II model (OSV-II model) in the present paper. The differences among the three versions models are clarified. Then, we derive an exact solution for the TSV model and that for the OSV-II model. Furthermore, we prove that the exact solution for the steady degree distribution of the TSV model and that of the OSV-II model are globally asymptotically stable. Based on the exact solutions, the differences of the solution of the degree distribution among the three versions models are analyzed.

Boolean networks have been widely used to model gene networks. However, such models are coarse-grained to an extent that they abstract away molecular specificities of gene regulation. Alternatively, bipartite Boolean network models of gene regulation explicitly distinguish genes from transcription factors (TFs). In such bipartite models, multiple TFs may simultaneously contribute to gene regulation by forming heteromeric complexes, thus giving rise to composition structures. Since bipartite Boolean models are relatively recent, an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising through heteromeric complexes. Moreover, we present an additional mechanism where composition structures may arise as a result of multiple TFs binding to cis-regulatory regions and provide empirical support for this mechanism. Next, we compare the restriction in BFs imposed by composition structures and by biologically meaningful properties. We find that though composition structures can severely restrict the number of Boolean functions (BFs) driving a gene, the two types of minimally complex BFs, namely nested canalyzing functions (NCFs) and read-once functions (RoFs), are comparatively more restrictive. Finally, we find that composition structures are highly enriched in real networks, but this enrichment most likely comes from NCFs and RoFs.

Collaboration with content sharing via digital maps is a type of application that is characteristic of the context of the social web. A malicious activity that is di cult to detect in this interactive context is the generation of a false trend on the map as the result of a plot in which several false reports by more than one person are done. In this paper, we describe how modeling complex networks of crime reported on a collaborative (or crowd) map can help identify regularities, and therefore show deviations arising from malicious activity. The idea here is to model a network comprised of users who reported crimes and the locations where such crimes were reported (e.g.: a census tract). Starting from a bipartite network model in which the vertices are individuals and census tracts, we projected a monopartite network of users in which the edges indicate the strength of connection between them. This connection strength indicates the degree of co-relatedness of the reports of crime made by these two users in a particular place. By characterizing this, we were able to observe that the relationships of non-hub users among themselves are typically no stronger than the relationship between such non-hub users and the hubs. If this happens, the evidence of malicious activity becomes clear. Simulation of malicious activities in this dataset has allowed evaluating the contributions and limitations of our approach.