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Register a new userLearning Latent Block Structure in Weighted Networks
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Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the networks large-scale structure, which can facilitate its scientific interpretation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by throwing away potentially useful information. We introduce the `weighted stochastic block model (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponential family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresholded. We describe a Bayesian variational algorithm for efficiently approximating this models posterior distribution over latent block structures. We then evaluate the WSBMs performance on both edge-existence and edge-weight prediction tasks for a set of real-world weighted networks. In all cases, the WSBM performs as well or better than the best alternatives on these tasks.
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Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic block models for multilayer and temporal networks; one of them uses nodes as its fundamental unit, whereas the other focuses on links. We also develop scalable algorithms for inferring the parameters of these models. Because our models describe all layers simultaneously, our approach takes full advantage of the information contained in the whole network when making predictions about any particular layer. We illustrate the potential of our approach by analyzing two empirical datasets---a temporal network of email communications, and a network of drug interactions for treating different cancer types. We find that modeling all layers simultaneously does result, in general, in more accurate link prediction. However, the most predictive model depends on the dataset under consideration; whereas the node-based model is more appropriate for predicting drug interactions, the link-based model is more appropriate for predicting email communication.
As new instances of nested organization --beyond ecological networks-- are discovered, scholars are debating around the co-existence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being solved, mainly for two reasons. First, nestedness and modularity appear to emerge from two contradictory dynamics, cooperation and competition. Second, existing methods to assess the presence of nestedness and modularity are flawed when it comes to the evaluation of concurrently nested and modular structures. In this work, we tackle the latter problem, presenting the concept of textit{in-block nestedness}, a structural property determining to what extent a network is composed of blocks whose internal connectivity exhibits nestedness. We then put forward a set of optimization methods that allow us to identify such organization successfully, both in synthetic and in a large number of real networks. These findings challenge our understanding of the topology of ecological and social systems, calling for new models to explain how such patterns emerge.
Originally a speculative pattern in ecological networks, the hybrid or compound nested-modular pattern has been confirmed, during the last decade, as a relevant structural arrangement that emerges in a variety of contexts --in ecological mutualistic system and beyond. This implies shifting the focus from the measurement of nestedness as a global property (macro level), to the detection of blocks (meso level) that internally exhibit a high degree of nestedness. Unfortunately, the availability and understanding of the methods to properly detect in-block nested partitions lie behind the empirical findings: while a precise quality function of in-block nestedness has been proposed, we lack an understanding of its possible inherent constraints. Specifically, while it is well known that Newman-Girvans modularity, and related quality functions, notoriously suffer from a resolution limit that impairs their ability to detect small blocks, the potential existence of resolution limits for in-block nestedness is unexplored. Here, we provide empirical, numerical and analytical evidence that the in-block nestedness function lacks a resolution limit, and thus our capacity to detect correct partitions in networks via its maximization depends solely on the accuracy of the optimization algorithms.
Identifying influential spreaders is crucial for understanding and controlling spreading processes on social networks. Via assigning degree-dependent weights onto links associated with the ground node, we proposed a variant to a recent ranking algorithm named LeaderRank [L. Lv et al., PLoS ONE 6 (2011) e21202]. According to the simulations on the standard SIR model, the weighted LeaderRank performs better than LeaderRank in three aspects: (i) the ability to find out more influential spreaders, (ii) the higher tolerance to noisy data, and (iii) the higher robustness to intentional attacks.
We use the information present in a bipartite network to detect cores of communities of each set of the bipartite system. Cores of communities are found by investigating statistically validated projected networks obtained using information present in the bipartite network. Cores of communities are highly informative and robust with respect to the presence of errors or missing entries in the bipartite network. We assess the statistical robustness of cores by investigating an artificial benchmark network, the co-authorship network, and the actor-movie network. The accuracy and precision of the partition obtained with respect to the reference partition are measured in terms of the adjusted Rand index and of the adjusted Wallace index respectively. The detection of cores is highly precise although the accuracy of the methodology can be limited in some cases.
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