Detecting niches of polarization in social media is a first step towards deploying mitigation strategies and avoiding radicalization. In this paper, we model polarization niches as close-knit dense communities of users, which are under the influence of some well-known sources of misinformation, and isolated from authoritative information sources. Based on this intuition we define the problem of finding a subgraph that maximizes a combination of ( i ) density, ( ii ) proximity to a small set of nodes A (named Attractors ), and ( iii ) distance from another small set of nodes R (named Repulsers ). Deviating from the bulk of the literature on detecting polarization, we do not exploit text mining or sentiment analysis, nor we track the propagation of information: we only exploit the network structure and the background knowledge about the sets A and R , which are given as input. We build on recent algorithmic advances in supermodular maximization to provide an iterative greedy algorithm, dubbed Down in the Hollow (dith), that converges fast to a near-optimal solution. Thanks to a novel theoretical upper bound, we are able to equip dith with a practical device that allows to terminate as soon as a solution with a user-specified approximation factor is found, making our algorithm very efficient in practice. Our experiments on very large networks confirm that our algorithm always returns a solution with an approximation factor better or equal to the one specified by the user, and it is scalable. Our case-studies in polarized settings, confirm the usefulness of our algorithmic primitive in detecting polarization niches.

Mining human-brain networks to discover patterns that can be used to discriminate between healthy individuals and patients affected by some neurological disorder, is a fundamental task in neuro-science. Learning simple and interpretable models is as important as mere classification accuracy. In this paper we introduce a novel approach for classifying brain networks based on extracting contrast subgraphs, i.e., a set of vertices whose induced subgraphs are dense in one class of graphs and sparse in the other. We formally define the problem and present an algorithmic solution for extracting contrast subgraphs. We then apply our method to a brain-network dataset consisting of children affected by Autism Spectrum Disorder and children Typically Developed. Our analysis confirms the interestingness of the discovered patterns, which match background knowledge in the neuro-science literature. Further analysis on other classification tasks confirm the simplicity, soundness, and high explainability of our proposal, which also exhibits superior classification accuracy, to more complex state-of-the-art methods.

Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far. As a first step in this direction, in this work, we study the problem of core decomposition of a multilayer network . Unlike the single-layer counterpart in which cores are all nested into one another and can be computed in linear time, the multilayer context is much more challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting, we devise three algorithms, which differ in the way they visit the core lattice and in their pruning techniques. We assess time and space efficiency of the three algorithms on a large variety of real-world multilayer networks. We then move a step forward and study the problem of extracting the inner-most (also known as maximal ) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. This allows for a consistent speed up over a naïve method that simply filters out non-inner-most ones from all the cores. Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks . We introduce a definition of multilayer densest subgraph that tradesoff between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting.