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Register a new userRevealing In-Block Nestedness: detection and benchmarking
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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.
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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.
The concept of nestedness, in particular for ecological and economical networks, has been introduced as a structural characteristic of real interacting systems. We suggest that the nestedness is in fact another way to express a mesoscale network property called the core-periphery structure. With real ecological mutualistic networks and synthetic model networks, we reveal the strong correlation between the nestedness and core-periphery-ness (likeness to the core-periphery structure), by defining the network-level measures for nestedness and core-periphery-ness in the case of weighted and bipartite networks. However, at the same time, via more sophisticated null-model analysis, we also discover that the degree (the number of connected neighbors of a node) distribution poses quite severe restrictions on the possible nestedness and core-periphery parameter space. Therefore, there must exist structurally interwoven properties in more fundamental levels of network formation, behind this seemingly obvious relation between nestedness and core-periphery structures.
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.
Time-stamped data are increasingly available for many social, economic, and information systems that can be represented as networks growing with time. The World Wide Web, social contact networks, and citation networks of scientific papers and online news articles, for example, are of this kind. Static methods can be inadequate for the analysis of growing networks as they miss essential information on the systems dynamics. At the same time, time-aware methods require the choice of an observation timescale, yet we lack principled ways to determine it. We focus on the popular community detection problem which aims to partition a networks nodes into meaningful groups. We use a multi-layer quality function to show, on both synthetic and real datasets, that the observation timescale that leads to optimal communities is tightly related to the systems intrinsic aging timescale that can be inferred from the time-stamped network data. The use of temporal information leads to drastically different conclusions on the community structure of real information networks, which challenges the current understanding of the large-scale organization of growing networks. Our findings indicate that before attempting to assess structural patterns of evolving networks, it is vital to uncover the timescales of the dynamical processes that generated them.
Research into detection of dense communities has recently attracted increasing attention within network science, various metrics for detection of such communities have been proposed. The most popular metric -- Modularity -- is based on the so-called rule that the links within communities are denser than external links among communities, has become the default. However, this default metric suffers from ambiguity, and worse, all augmentations of modularity and based on a narrow intuition of what it means to form a community. We argue that in specific, but quite common systems, links within a community are not necessarily more common than links between communities. Instead we propose that the defining characteristic of a community is that links are more predictable within a community rather than between communities. In this paper, based on the effect of communities on link prediction, we propose a novel metric for the community detection based directly on this feature. We find that our metric is more robustness than traditional modularity. Consequently, we can achieve an evaluation of algorithm stability for the same detection algorithm in different networks. Our metric also can directly uncover the false community detection, and infer more statistical characteristics for detection algorithms.
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