Construction and analysis of multi-relationship bipartite network model

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.

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.

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.

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.

Distribution characteristics of weighted bipartite evolving networks

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.

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.

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.

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.

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.

ObjectiveOur objective was to use multiple romantic relationship dimensions to identify a typology of emerging adult romantic relationships.BackgroundEmerging adult romantic relationships vary in terms of their relational dynamics, emotional and physical intimacy, and commitment. Understanding the diversity in emerging adult romantic relationships is crucial for developing effective relationship education for emerging adults as they make decisions about their romantic partnerships.MethodUsing data from 396 romantically involved but unmarried emerging adults, we used cluster analysis to identify a typology of romantic relationships based on relational dynamics (i.e., warmth and support and negative interactions), relationship duration, consolidation (i.e., number of nights and percentage of free time spent together), and commitment (i.e., likelihood of marrying partner).ResultsThe results indicated five types of relationships: (a) happily consolidated (30.8%), (b) happily independent (18.9%), (c) exploratory (17.9%), (d) stuck (23.0%), and (e) high intensity (9.3%). Demographic characteristics, depressive symptoms, life satisfaction, current cohabitation, and cycling within the current relationship varied between the relationship types.ConclusionsThere appear to be meaningful and important variations among the types of romantic relationships that emerging adults pursue. The associations between relationship type and well‐being depends on the interplay between relational dynamics, consolidation, and commitment.ImplicationsIndividuals in different types of relationships may require targeted interventions to help them move out of problematic relationships or to help them build skills for developing and maintaining relationship quality. Suggestions for each type of relationship are provided.

Finding different types of communities has become a research hot spot in network science. Plenty of the real-world systems containing different types of objects and relationships can be perfectly described as the heterogeneous networks. However, most of the current research on community detection is applied for the homogeneous networks, while there is no effective function to quantify the quality of the community structure in heterogeneous networks. In this paper, we first propose the null model with the same heterogeneous node degree distribution of the original heterogeneous networks. The probability of there being an edge between two nodes is given to build the modularity function of the heterogeneous networks. Based on our modularity function, a fast algorithm of community detection is proposed for the large scale heterogeneous networks. We use the algorithm to detect the communities in the real-world twitter event networks. The experimental results show that our method perform better than other exciting algorithms and demonstrate that the modularity function of the heterogeneous networks is an effective parameter that can be used to quantify the quality of the community structure in heterogeneous networks.

Heterogeneous information networks have drawn much attention in recent years due to their significant applications, such as text mining, e-commerce, social networks, and bioinformatics. Clustering different types of objects simultaneously based upon not only their relations of the same type, but also the relations between different types of objects can improve the clustering quality mutually. In this paper, we propose a general model, in which both the homogeneous and heterogeneous relations are considered simultaneously, to describe the structure of the heterogeneous information networks and devise a novel parametric free multi-type overlapped clustering approach. In this model, different types of relations between different types of objects are represented by a group of matrices. In this way, we transfer the multi-type clustering problem into the information compression problem. Subsequently, greedy search approaches, which aim at describing the group of relational matrices with least bits, are proposed. Moreover, by discovering the discriminative clusters among different types of objects, we devise effective parameter-free strategies to discover either overlapping or non-overlapping structure among different types of clusters. Extensive experiments on real-world and synthetic data sets demonstrate our methods are effective and efficient.

A major mining task for binary matrixes is the extraction of approximate top-k patterns that are able to concisely describe the input data. The top-k pattern discovery problem is commonly stated as an optimization one, where the goal is to minimize a given cost function, e.g., the accuracy of the data description. In this work, we review several greedy algorithms, and discuss PaNDa+, an algorithmic framework able to optimize different cost functions generalized into a unifying formulation. We evaluated the goodness of the algorithm by measuring the quality of the extracted patterns. We adapted standard quality measures to assess the capability of the algorithm to discover both the items and transactions of the patterns embedded in the data. The evaluation was conducted on synthetic data, where patterns were artificially embedded, and on real-world text collection, where each document is labeled with a topic. Finally, in order to qualitatively evaluate the usefulness of the discovered patterns, we exploited PaNDa+ to detect overlapping communities in a bipartite network. The results show that PaNDa+ is able to discover high-quality patterns in both synthetic and real-world datasets.