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Register a new userMeasuring and Modeling Bipartite Graphs with Community Structure
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Network science is a powerful tool for analyzing complex systems in fields ranging from sociology to engineering to biology. This paper is focused on generative models of large-scale bipartite graphs, also known as two-way graphs or two-mode networks. We propose two generative models that can be easily tuned to reproduce the characteristics of real-world networks, not just qualitatively, but quantitatively. The characteristics we consider are the degree distributions and the metamorphosis coefficient. The metamorphosis coefficient, a bipartite analogue of the clustering coefficient, is the proportion of length-three paths that participate in length-four cycles. Having a high metamorphosis coefficient is a necessary condition for close-knit community structure. We define edge, node, and degreewise metamorphosis coefficients, enabling a more detailed understanding of the bipartite connectivity that is not explained by degree distribution alone. Our first model, bipartite Chung-Lu (CL), is able to reproduce real-world degree distributions, and our second model, bipartite block two-level Erdos-Renyi (BTER), reproduces both the degree distributions as well as the degreewise metamorphosis coefficients. We demonstrate the effectiveness of these models on several real-world data sets.
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Understanding the network structure, and finding out the influential nodes is a challenging issue in the large networks. Identifying the most influential nodes in the network can be useful in many applications like immunization of nodes in case of epidemic spreading, during intentional attacks on complex networks. A lot of research is done to devise centrality measures which could efficiently identify the most influential nodes in the network. There are two major approaches to the problem: On one hand, deterministic strategies that exploit knowledge about the overall network topology in order to find the influential nodes, while on the other end, random strategies are completely agnostic about the network structure. Centrality measures that can deal with a limited knowledge of the network structure are required. Indeed, in practice, information about the global structure of the overall network is rarely available or hard to acquire. Even if available, the structure of the network might be too large that it is too much computationally expensive to calculate global centrality measures. To that end, a centrality measure is proposed that requires information only at the community level to identify the influential nodes in the network. Indeed, most of the real-world networks exhibit a community structure that can be exploited efficiently to discover the influential nodes. We performed a comparative evaluation of prominent global deterministic strategies together with stochastic strategies with an available and the proposed deterministic community-based strategy. Effectiveness of the proposed method is evaluated by performing experiments on synthetic and real-world networks with community structure in the case of immunization of nodes for epidemic control.
Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts, existing approaches to bipartite community detection have drawbacks, including implicit parameter choices, loss of information through one-mode projections, and lack of interpretability. Here we solve the community detection problem for bipartite networks by formulating a bipartite stochastic block model, which explicitly includes vertex type information and may be trivially extended to $k$-partite networks. This bipartite stochastic block model yields a projection-free and statistically principled method for community detection that makes clear assumptions and parameter choices and yields interpretable results. We demonstrate this models ability to efficiently and accurately find community structure in synthetic bipartite networks with known structure and in real-world bipartite networks with unknown structure, and we characterize its performance in practical contexts.
In the era of big data, graph sampling is indispensable in many settings. Existing sampling methods are mostly designed for static graphs, and aim to preserve basic structural properties of the original graph (such as degree distribution, clustering coefficient etc.) in the sample. We argue that for any sampling method it is impossible to produce an universal representative sample which can preserve all the properties of the original graph; rather sampling should be application specific (such as preserving hubs - needed for information diffusion). Here we consider community detection as an application scenario. We propose ComPAS, a novel sampling strategy that unlike previous methods, is not only designed for streaming graphs (which is a more realistic representation of a real-world scenario) but also preserves the community structure of the original graph in the sample. Empirical results on both synthetic and different real-world graphs show that ComPAS is the best to preserve the underlying community structure with average performance reaching 73.2% of the most informed algorithm for static graphs.
We introduce a new conception of community structure, which we refer to as hidden community structure. Hidden community structure refers to a specific type of overlapping community structure, in which the detection of weak, but meaningful, communities is hindered by the presence of stronger communities. We present Hidden Community Detection HICODE, an algorithm template that identifies both the strong, dominant community structure as well as the weaker, hidden community structure in networks. HICODE begins by first applying an existing community detection algorithm to a network, and then removing the structure of the detected communities from the network. In this way, the structure of the weaker communities becomes visible. Through application of HICODE, we demonstrate that a wide variety of real networks from different domains contain many communities that, though meaningful, are not detected by any of the popular community detection algorithms that we consider. Additionally, on both real and synthetic networks containing a hidden ground-truth community structure, HICODE uncovers this structure better than any baseline algorithms that we compared against. For example, on a real network of undergraduate students that can be partitioned either by `Dorm (residence hall) or `Year, we see that HICODE uncovers the weaker `Year communities with a JCRecall score (a recall-based metric that we define in the text) of over 0.7, while the baseline algorithms achieve scores below 0.2.
Random graph models are important constructs for data analytic applications as well as pure mathematical developments, as they provide capabilities for network synthesis and principled analysis. Several models have been developed with the aim of faithfully preserving important graph metrics and substructures. With the goal of capturing degree distribution, clustering coefficient, and communities in a single random graph model, we propose a new model to address shortcomings in a progression of network modeling capabilities. The Block Two-Level Erd{H{o}}s-R{e}nyi (BTER) model of Seshadhri et al., designed to allow prescription of expected degree and clustering coefficient distributions, neglects community modeling, while the Generalized BTER (GBTER) model of Bridges et al., designed to add community modeling capabilities to BTER, struggles to faithfully represent all three characteristics simultaneously. In this work, we fit BTER and two GBTER configurations to several real-world networks and compare the results with that of our new model, the Extended GBTER (EGBTER) model. Our results support that EBGTER adds a community-modeling flexibility to BTER, while retaining a satisfactory level of accuracy in terms of degree and clustering coefficient. Our insights and empirical testing of previous models as well as the new model are novel contributions to the literature.
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