Bipartite Network Structure Research Articles

The structure of bacteria-fungi bipartite networks along elevational gradients in contrasting climates.

Climate change is altering species distribution and modifying interactions in microbial communities. Understanding microbial community structure and their interactions is crucial to interpreting ecosystem responses to climate change. Here, we examined the assemblages of stream bacteria and fungi, and the associations between the two groups along elevational gradients in two regions with contrasting precipitation and temperature, that is the Galong and Qilian mountains of the Tibetan Plateau. In the wetter and warmer region, the species richness significantly increased and decreased with elevation for bacteria and fungi, respectively, while were nonsignificant in the drier and colder region. Their bipartite network structure was also different by showing significant increases in connectance and nestedness towards higher elevations only in the wetter and warmer region. In addition, these correlation network structure generally exhibited similar positive association with species richness in the wetter and warmer region and the drier and colder region. In the wetter and warmer region, climatic change along elevation was more important in determining connectance and nestedness, whereas microbial species richness exerted a stronger influence on network structure and robustness in the drier and colder region. These findings indicate substantial forthcoming changes in microbial diversity and network structure in warming climates, especially in wetter and warmer regions on Earth, advancing the understanding of microbial bipartite interactions' response to climate change.

Link prediction in bipartite networks via effective integration of explicit and implicit relations

Link prediction in bipartite networks aims to identify or predict possible links between nodes of different types based on known network information. However, most existing studies predominantly focus on monopartite networks, neglecting the intrinsic properties unique to bipartite networks, such as the intricate high-order relationships between nodes. Both explicit relations (representing low-order information) and implicit relations (representing high-order information) play essential roles in predicting the evolution of bipartite networks, and they are indispensable and mutually reinforce each other. To fully leverage their potential in addressing the link prediction problem, we propose a novel framework from the perspective of network representation. This framework not only effectively integrates explicit relations and implicit relations, but also preserves the local and global structure of bipartite networks. Specifically, the probability of a link between two nodes of different types is determined by the linear sum of the contribution values of the mutually connected nodes in their respective common neighbors. Implicit relations are then used to preserve the local structure during the network representation. Furthermore, we implement optimization using a relaxed majorization-minimization algorithm, offering the advantage of uncovering high-quality local minima. Our proposed framework has undergone extensive testing on eight real-world datasets, and the results unequivocally demonstrate its significant superiority over state-of-the-art methods.

The diffusion of health care fraud: A bipartite network analysis

Many studies have examined the diffusion of health care innovation but less is known about the diffusion of health care fraud. In this paper, we consider the diffusion of potentially fraudulent Medicare home health care billing in the United States during 2002–16, with a focus on the 21 hospital referral regions (HRRs) covered by local Department of Justice (DOJ) anti-fraud “strike force” offices. We hypothesize that patient-sharing across home health care agencies (HHAs) provides a mechanism for the rapid diffusion of fraudulent strategies. We measure such activity using a novel bipartite mixture (or BMIX) network index, which captures patient sharing across multiple agencies and thus conveys more information about the diffusion process than conventional unipartite network measures. Using a complete population of fee-for-service Medicare claims data, we first find a remarkable increase in home health care activity between 2002 and 2009 in many regions targeted by the DOJ; average billing per Medicare enrollee in McAllen TX and Miami increased by $2127 and $2422 compared to just an average $289 increase in other HRRs not targeted by the DOJ. Second, we establish that the HRR-level BMIX (but not other network measures) was a strong predictor of above-average home health care expenditures across HRRs. Third, within HRRs, agencies sharing more patients with other agencies were predicted to increase billing. Finally, the initial 2002 BMIX index was a strong predictor of subsequent changes in HRR-level home health billing during 2002–9. These results highlight the importance of bipartite network structure in diffusion and in infection and contagion models more generally.

Tail probabilities of random linear functions of regularly varying random vectors

We provide a new extension of Breiman’s Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a characterization of regular variation on cones in \([0,\infty )^d\) under random linear transformations. This allows us to compute probabilities of a variety of tail events, which classical multivariate regularly varying models would report to be asymptotically negligible. We illustrate our findings with applications to risk assessment in financial systems and reinsurance markets under a bipartite network structure.

Deep Link-Prediction Based on the Local Structure of Bipartite Networks

Link prediction based on bipartite networks can not only mine hidden relationships between different types of nodes, but also reveal the inherent law of network evolution. Existing bipartite network link prediction is mainly based on the global structure that cannot analyze the role of the local structure in link prediction. To tackle this problem, this paper proposes a deep link-prediction (DLP) method by leveraging the local structure of bipartite networks. The method first extracts the local structure between target nodes and observes structural information between nodes from a local perspective. Then, representation learning of the local structure is performed on the basis of the graph neural network to extract latent features between target nodes. Lastly, a deep-link prediction model is trained on the basis of latent features between target nodes to achieve link prediction. Experimental results on five datasets showed that DLP achieved significant improvement over existing state-of-the-art link prediction methods. In addition, this paper analyzes the relationship between local structure and link prediction, confirming the effectiveness of a local structure in link prediction.

Eigenvalue-based entropy and spectrum of bipartite digraph

Graph entropy is an important measure of the evolution and complexity of networks. Bipartite graph is a special network and an important mathematical model for system resource allocation and management. In reality, a network system usually has obvious directionality. The direction of the network, or the movement trend of the network, can be described with spectrum index. However, little research has been done on the eigenvalue-based entropy of directed bipartite network. In this study, based on the adjacency matrix, the in-degree Laplacian matrix and the in-degree signless Laplacian matrix of directed bipartite graph, we defined the eigenvalue-based entropy for the directed bipartite network. Using the eigenvalue-based entropy, we described the evolution law of the directed bipartite network structure. Aiming at the direction and bipartite feature of the directed bipartite network, we improved the generation algorithm of the undirected network. We then constructed the directed bipartite nearest-neighbor coupling network, directed bipartite small-world network, directed bipartite scale-free network, and directed bipartite random network. In the proposed model, spectrum of those directed bipartite network is used to describe the directionality and bipartite property. Moreover, eigenvalue-based entropy is empirically studied on a real-world directed movie recommendation network, in which the law of eigenvalue-base entropy is observed. That is, if eigenvalue-based entropy value of the recommendation system is large, the evolution of movie recommendation network becomes orderless. While if eigenvalue-based entropy value is small, the structural evolution of the movie recommendation network tends to be regular. The simulation experiment shows that eigenvalue-based entropy value in the real directed bipartite network is between the values of a directed bipartite small world and a scale-free network. It shows that the real directed bipartite network has the structural property of the two typical directed bipartite networks. The coexistence of the small-world phenomena and the scale-free phenomena in the real network is consistent with the evolution law of typical network models. The experimental results show that the validity and rationality of the definition of eigenvalue-based entropy, which serves as a tool in the analysis of directed bipartite networks.

Network and Cluster Analysis of the Funding Relationship among the U.N. Agencies and State Donors

The purpose of this study is to examine the network structure of the world polity with the funding data of the United Nations agencies and their donor states in 2020. Network analysis was employed to further understand the current structure of the network from the world systems approach. Research hypotheses concerning the theory were developed from a network and hierarchical perspective on political science. Considering the bipartite network structure of data, cohesion measures including density, average distance, diameter, and fragmentation were calculated. In addition, the K-means clustering was conducted to examine the world structure. The results of network analysis suggest that the global structure is partly aligned with the world systems theory. The findings demonstrate that both states and agency actors are interconnected to each other, and its structure is being polarized and the power is centralized to core countries. This study sheds light on the funding relationship among states and U.N. agencies as a function of international governance.

Refinement for community structures of bipartite networks

Bipartite networks composed of dichotomous node sets are ubiquitous in nature and society. Partly for simplicity’s sake, many studies have focused on their projection onto their unipartite versions where one only needs to care about a single type of node. When it comes to mesoscale structures such as communities, however, properly incorporating a priori structural restrictions such as bipartivity is ever more important. In this paper, as a case study, we take the community structure of bipartite networks in various scales to examine the amount of information of bipartivity encoded in the community detection procedure. In particular, we report the robustness in reliability of detected community based on consistency by comparing the detection algorithm with or without the consideration of bipartivity. From the analysis with model networks embedding prescribed communities and real networks, we find that the community detection tailored to take the bipartivity into account clearly yields more robust community structures than the one without such structural information. This demonstrates the necessity for customizing the community detection algorithm by encoding whatever information is known about networks of interest and, at the same time, raises an interesting question on the possibility of estimating the quantitative amount of information from such a customization.

Joint nonnegative matrix factorization and network embedding for graph co-clustering

Graph co-clustering aims to simultaneously group heterogeneous vertices in bipartite networks. The current algorithms measure similarity of vertices by either topology or latent feature of networks, which is insufficient to fully characterize the structure of bipartite graphs. To overcome this problem, we propose a novel co-clustering algorithm by jointly integrating network embedding and NMF (called NENMF) based on the fact that graph representation learning implicitly implies matrix factorizations, where multiple views of bipartite networks are integrated for graph co-clustering. Specifically, the equivalence between nonnegative matrix factorization (NMF) graph embedding for co-clustering is proven, which serves as the theoretical foundation for the proposed algorithm. Then, two auxiliary graphs are generated to fully characterize the topology structure of bipartite networks. Finally, NENMF jointly learns low-rank approximation matrices for bipartite networks and network embedding of auxiliary graphs, where network embedding is regularized into objective function of NMF. The main advantage of the proposed algorithm is to boost the accuracy by combining the low-dimensional approximation and graph representation of bipartite networks without increasing time complexity. The experimental results demonstrate that NENMF outperforms state-of-the-art approaches in terms of accuracy.

Mediated Remote Synchronization of Kuramoto-Sakaguchi Oscillators: The Number of Mediators Matters

Cortical regions without direct neuronal connections have been observed to exhibit synchronized dynamics. A recent empirical study has further revealed that such regions that share more common neighbors are more likely to behave coherently. To analytically investigate the underlying mechanisms, we consider that a set of n oscillators, which have no direct connections, are linked through m intermediate oscillators (called mediators), forming a complete bipartite network structure. Modeling the oscillators by the Kuramoto-Sakaguchi model, we rigorously prove that mediated remote synchronization, i.e., synchronization between those n oscillators that are not directly connected, becomes more robust as the number of mediators increases. Simulations are also carried out to show that our theoretical findings can be applied to other general and complex networks.

Continual representation learning for evolving biomedical bipartite networks.

Many real-world biomedical interactions such as 'gene-disease', 'disease-symptom' and 'drug-target' are modeled as a bipartite network structure. Learning meaningful representations for such networks is a fundamental problem in the research area of Network Representation Learning (NRL). NRL approaches aim to translate the network structure into low-dimensional vector representations that are useful to a variety of biomedical applications. Despite significant advances, the existing approaches still have certain limitations. First, a majority of these approaches do not model the unique topological properties of bipartite networks. Consequently, their straightforward application to the bipartite graphs yields unsatisfactory results. Second, the existing approaches typically learn representations from static networks. This is limiting for the biomedical bipartite networks that evolve at a rapid pace, and thus necessitate the development of approaches that can update the representations in an online fashion. In this research, we propose a novel representation learning approach that accurately preserves the intricate bipartite structure, and efficiently updates the node representations. Specifically, we design a customized autoencoder that captures the proximity relationship between nodes participating in the bipartite bicliques (2 × 2 sub-graph), while preserving both the global and local structures. Moreover, the proposed structure-preserving technique is carefully interleaved with the central tenets of continual machine learning to design an incremental learning strategy that updates the node representations in an online manner. Taken together, the proposed approach produces meaningful representations with high fidelity and computational efficiency. Extensive experiments conducted on several biomedical bipartite networks validate the effectiveness and rationality of the proposed approach.

Dynamical behaviors of a vector-borne diseases model with two time delays on bipartite networks.

In order to study the impact of the incubation periods of humans and vectors on diseases transmission, a novel vector-borne diseases model with two time delays on bipartite networks is proposed. The formula of the basic reproduction number R0 is given, which is dependent on time delays. Moreover, the globally asymptotic stability of the disease-free equilibrium and the endemic equilibrium is proved by constructing appropriate Lyapunov functions. Finally, numerical simulations are carried out to verify the analysis results and reveal the influence of the structure of bipartite networks on the basic reproduction number.

BurstBiRank: Co-Ranking Developers and Projects in GitHub with Complex Network Structures and Bursty Interactions

With the wide adoption of social collaborative coding, more and more developers participate and collaborate on platforms such as GitHub through rich social and technical relationships, forming a large-scale complex technical system. Like the functionalities of critical nodes in other complex systems, influential developers and projects usually play an important role in driving this technical system to more optimized states with higher efficiency for software development, which makes it a meaningful research direction on identifying influential developers and projects in social collaborative coding platforms. However, traditional ranking methods seldom take into account the continuous interactions and the driving forces of human dynamics. In this paper, we combine the bursty interactions and the bipartite network structure between developers and projects and propose the BurstBiRank model. Firstly, the burstiness between each pair of developers and projects is calculated. Secondly, a weighted developer-project bipartite network is constructed using the burstiness as weight. Finally, an iterative score diffusion process is applied to this bipartite network and a final ranking score is obtained at the stationary state. The real-world case study on GitHub demonstrates the effectiveness of our proposed BurstBiRank and the outperformance of traditional ranking methods.

Mapping flows on bipartite networks.

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.

Myco- and photobiont associations in crustose lichens in the McMurdo Dry Valleys (Antarctica) reveal high differentiation along an elevational gradient

Climatically extreme regions such as the polar deserts of the McMurdo Dry Valleys (78° S) in Continental Antarctica are key areas for a better understanding of changes in ecosystems. Therefore, it is particularly important to analyze and communicate current patterns of biodiversity in these sensitive areas, where precipitation mostly occurs in form of snow and liquid water is rare. Humidity provided by dew, clouds, and fog are the main water sources, especially for rock-dwelling crustose lichens as one of the most common vegetation-forming organisms. We investigated the diversity and interaction specificity of myco-/photobiont associations of 232 crustose lichen specimens, collected along an elevational gradient (171–959 m a.s.l.) within the McMurdo Dry Valleys. The mycobiont species and photobiont OTUs were identified by using three markers each (nrITS, mtSSU, RPB1, and nrITS, psbJ-L, COX2). Elevation, positively associated with water availability, turned out to be the key factor explaining most of the distribution patterns of the mycobionts. Pairwise comparisons showed Lecidea cancriformis and Rhizoplaca macleanii to be significantly more common at higher elevations and Carbonea vorticosa and Lecidea polypycnidophora at lower elevations. Lichen photobionts were dominated by the globally distributed Trebouxia OTU, Tr_A02 which occurred at all habitats. Network specialization resulting from myco-/photobiont bipartite network structure varied with elevation and associated abiotic factors. Along an elevational gradient, the spatial distribution, diversity, and genetic variability of the lichen symbionts appear to be mainly influenced by improved water relations at higher altitudes.

Community detection in bipartite networks with stochastic block models.

In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in bipartite networks which parsimoniously chooses the number of communities. The biSBM improves community detection results over general SBMs when data are noisy, improves the model resolution limit by a factor of sqrt[2], and expands our understanding of the complicated optimization landscape associated with community detection tasks. A direct comparison of certain terms of the prior distributions in the biSBM and a related high-resolution hierarchical SBM also reveals a counterintuitive regime of community detection problems, populated by smaller and sparser networks, where nonhierarchical models outperform their more flexible counterpart.

Identifying key players in bipartite networks

AbstractMeasures of bipartite network structure have recently gained attention from network scholars. However, there is currently no measure for identifying key players in two-mode networks. This article proposes measures for identifying key players in bipartite networks. It focuses on two measures: fragmentation and cohesion centrality. It extends the centrality measures to bipartite networks by considering (1) cohesion and fragmentation centrality within a one-mode projection, (2) cross-modal cohesion and fragmentation centrality, where a node in one mode is influential in the one-mode projection of the other mode, and (3) cohesion and fragmentation centrality across the entire bipartite structure. Empirical examples are provided for the Southern Women’s data and on the Ndrangheta mafia data.

Motifs in bipartite ecological networks: uncovering indirect interactions

Indirect interactions play an essential role in governing population, community and coevolutionary dynamics across a diverse range of ecological communities. Such communities are widely represented as bipartite networks: graphs depicting interactions between two groups of species, such as plants and pollinators or hosts and parasites. For over thirty years, studies have used indices, such as connectance and species degree, to characterise the structure of these networks and the roles of their constituent species. However, compressing a complex network into a single metric necessarily discards large amounts of information about indirect interactions. Given the large literature demonstrating the importance and ubiquity of indirect effects, many studies of network structure are likely missing a substantial piece of the ecological puzzle. Here we use the emerging concept of bipartite motifs to outline a new framework for bipartite networks that incorporates indirect interactions. While this framework is a significant departure from the current way of thinking about bipartite ecological networks, we show that this shift is supported by analyses of simulated and empirical data. We use simulations to show how consideration of indirect interactions can highlight differences missed by the current index paradigm that may be ecologically important. We extend this finding to empirical plant–pollinator communities, showing how two bee species, with similar direct interactions, differ in how specialised their competitors are. These examples underscore the need to not rely solely on network‐ and species‐level indices for characterising the structure of bipartite ecological networks.

Warm-glow giving in networks with multiple public goods

This paper explores a voluntary contribution game in the presence of warm-glow effects. There are many public goods and each public good benefits a different group of players. The structure of the game induces a bipartite network structure, where players are listed on one side and the public good groups they form are listed on the other side. The main result of the paper shows the existence and uniqueness of a Nash equilibrium. The unique Nash equilibrium is also shown to be asymptotically stable. Then the paper provides some comparative statics analysis regarding pure redistribution, taxation and subsidies. It appears that small redistributions of wealth may sometimes be neutral, but generally, the effects of redistributive policies depend on how public good groups are related in the contribution network structure.

Coevolution leaves a weak signal on ecological networks

AbstractOne of the major challenges in evolutionary ecology is to understand how coevolution shapes species interaction networks. Important topological properties of networks such as nestedness and modularity are thought to be affected by coevolution. However, there has been no test whether coevolution does, in fact, lead to predictable network structure. Here, we investigate the structure of simulated bipartite networks generated under different modes of coevolution. We ask whether evolutionary processes influence network structure and, furthermore, whether any emergent trends are influenced by the strength or “intimacy” of the species interactions. We find that coevolution leaves a weak and variable signal on network topology, particularly nestedness and modularity, which was not strongly affected by the intimacy of interactions. Our findings indicate that network metrics, on their own, should not be used to make inferences about processes underlying the evolutionary history of communities. Instead, a more holistic approach that combines network approaches with traditional phylogenetic and biogeographic reconstructions is needed.