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Register a new userMeasuring the effect of node aggregation on community detection
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Many times the nodes of a complex network, whether deliberately or not, are aggregated for technical, ethical, legal limitations or privacy reasons. A common example is the geographic position: one may uncover communities in a network of places, or of individuals identified with their typical geographical position, and then aggregate these places into larger entities, such as municipalities, thus obtaining another network. The communities found in the networks obtained at various levels of aggregation may exhibit various degrees of similarity, from full alignment to perfect independence. This is akin to the problem of ecological and atomic fallacies in statistics, or to the Modified Areal Unit Problem in geography. We identify the class of community detection algorithms most suitable to cope with node aggregation, and develop an index for aggregability, capturing to which extent the aggregation preserves the community structure. We illustrate its relevance on real-world examples (mobile phone and Twitter reply-to networks). Our main message is that any node-partitioning analysis performed on aggregated networks should be interpreted with caution, as the outcome may be strongly influenced by the level of the aggregation.
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Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the network, is able to preserve some interesting features generally observed in real-world networks such as heterogeneity in the degree distribution, high clustering coefficient, and small-world effect. Moreover, the angular distribution of the nodes in the hyperbolic plane reveals a community structure of the embedded network. It is worth noting that, while a large body of literature compares well-known community detection algorithms, there is still no consensus on what defines an ideal community partition on a network. Moreover, heuristics for communities found on networks embedded in the hyperbolic space have been investigated here for the first time. We compare the partitions found on embedded networks to the partitions obtained before the embedding step, both for a synthetic network and for two real-world networks. The second part of this paper presents the application of our pipeline to a network of retweets in the context of the Italian elections. Our results uncover a community structure reflective of the political spectrum, encouraging further research on the application of community detection heuristics to graphs mapped onto hyperbolic planes.
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.
Many systems exhibit complex temporal dynamics due to the presence of different processes taking place simultaneously. Temporal networks provide a framework to describe the time-resolve interactions between components of a system. An important task when investigating such systems is to extract a simplified view of the temporal network, which can be done via dynamic community detection or clustering. Several works have generalized existing community detection methods for static networks to temporal networks, but they usually rely on temporal aggregation over time windows, the assumption of an underlying stationary process, or sequences of different stationary epochs. Here, we derive a method based on a dynamical process evolving on the temporal network and restricted by its activation pattern that allows to consider the full temporal information of the system. Our method allows dynamics that do not necessarily reach a steady state, or follow a sequence of stationary states. Our framework encompasses several well-known heuristics as special cases. We show that our method provides a natural way to disentangle the different natural dynamical scales present in a system. We demonstrate our method abilities on synthetic and real-world examples.
Community detection is expensive, and the cost generally depends at least linearly on the number of vertices in the graph. We propose working with a reduced graph that has many fewer nodes but nonetheless captures key community structure. The K-core of a graph is the largest subgraph within which each node has at least K connections. We propose a framework that accelerates community detection by applying an expensive algorithm (modularity optimization, the Louvain method, spectral clustering, etc.) to the K-core and then using an inexpensive heuristic (such as local modularity maximization) to infer community labels for the remaining nodes. Our experiments demonstrate that the proposed framework can reduce the running time by more than 80% while preserving the quality of the solutions. Recent theoretical investigations provide support for using the K-core as a reduced representation.
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.
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