Framework for Clique-based Fusion of Graph Streams in Multi-function System Testing

The paper describes a framework for multi-function system testing. Multi-function system testing is considered as fusion (or revelation) of clique-like structures. The following sets are considered: (i) subsystems (system parts or units / components / modules), (ii) system functions and a subset of system components for each system function, and (iii) function clusters (some groups of system functions which are used jointly). Test procedures (as units testing) are used for each subsystem. The procedures lead to an ordinal result (states, colors) for each component, e.g., [1,2,3,4] (where 1 corresponds to 'out of service', 2 corresponds to 'major faults', 3 corresponds to 'minor faults', 4 corresponds to 'trouble free service'). Thus, for each system function a graph over corresponding system components is examined while taking into account ordinal estimates/colors of the components. Further, an integrated graph (i.e., colored graph) for each function cluster is considered (this graph integrates the graphs for corresponding system functions). For the integrated graph (for each function cluster) structure revelation problems are under examination (revelation of some subgraphs which can lead to system faults): (1) revelation of clique and quasi-clique (by vertices at level 1, 2, etc.; by edges/interconnection existence) and (2) dynamical problems (when vertex colors are functions of time) are studied as well: existence of a time interval when clique or quasi-clique can exist. Numerical examples illustrate the approach and problems.Comment: 6 pages, 13 figure

Mining the Largest Quasi-clique in Human Protein Interactome

A clique is a complete subgraph of a graph. Often, a clique is interpreted as a dense module of vertices within a graph. However, in many real-world situations, the classical problem of finding a clique is required to be relaxed. This motivates the problem of finding quasicliques that are almost complete subgraphs of a graph. In sparse and very large scale-free networks, the problem of finding the largest quasi-clique becomes hard to manage with the existing approaches. Here, we propose a heuristic algorithm in this paper for locating the largest quasi-clique from the human protein-protein interaction networks. The results show promise in computational biology research by the exploration of significant protein modules

Extraction sous Contraintes d'Ensembles de Cliques Homogènes

Document sur site LIRIS : http://liris.cnrs.fr/Documents/Liris-4915.pdfNational audienceNous proposons une méthode de fouille de données sur des graphes ayant un ensemble d'étiquettes associé à chaque sommet. Une application est, par exemple, d'analyser un réseau social de chercheurs co-auteurs lorsque des étiquettes précisent les conférences dans lesquelles ils publient.Nous définissons l'extraction sous contraintes d'ensembles de cliques tel que chaque sommet des cliques impliquées partage suffisamment d'étiquettes. Nous proposons une méthode pour calculer tous les Ensembles Maximaux de Cliques dits Homogènes qui satisfont une conjonction de contraintes fixée par l'analyste et concernant le nombre de cliques séparées, la taille des cliques ainsi que le nombre d'étiquettes partagées. Les expérimentations montrent que l'approche fonctionne sur de grands graphes construits à partir de données réelles et permet la mise en évidence de structures intéressantes

Cores and Other Dense Structures in Complex Networks

Complex networks are a powerful paradigm to model complex systems. Specific network models, e.g., multilayer networks, temporal networks, and signed networks, enrich the standard network representation with additional information to better capture real-world phenomena. Despite the keen interest in a variety of problems, algorithms, and analysis methods for these types of network, the problem of extracting cores and dense structures still has unexplored facets. In this work, we present advancements to the state of the art by the introduction of novel definitions and algorithms for the extraction of dense structures from complex networks, mainly cores. At first, we define core decomposition in multilayer networks together with a series of applications built on top of it, i.e., the extraction of maximal multilayer cores only, densest subgraph in multilayer networks, the speed-up of the extraction of frequent cross-graph quasi-cliques, and the generalization of community search to the multilayer setting. Then, we introduce the concept of core decomposition in temporal networks; also in this case, we are interested in the extraction of maximal temporal cores only. Finally, in the context of discovering polarization in large-scale online data, we study the problem of identifying polarized communities in signed networks. The proposed methodologies are evaluated on a large variety of real-world networks against na\"{\i}ve approaches, non-trivial baselines, and competing methods. In all cases, they show effectiveness, efficiency, and scalability. Moreover, we showcase the usefulness of our definitions in concrete applications and case studies, i.e., the temporal analysis of contact networks, and the identification of polarization in debate networks.Comment: arXiv admin note: text overlap with arXiv:1812.0871

Assessing the Computational Complexity of Multi-Layer Subgraph Detection

Multi-layer graphs consist of several graphs (layers) over the same vertex set. They are motivated by real-world problems where entities (vertices) are associated via multiple types of relationships (edges in different layers). We chart the border of computational (in)tractability for the class of subgraph detection problems on multi-layer graphs, including fundamental problems such as maximum matching, finding certain clique relaxations (motivated by community detection), or path problems. Mostly encountering hardness results, sometimes even for two or three layers, we can also spot some islands of tractability

Explainable Classification of Brain Networks via Contrast Subgraphs

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 neuroscience. 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 neuroscience 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.Comment: To be published at KDD 202

Core Decomposition in Multilayer Networks: Theory, Algorithms, and Applications

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. In this work we study the problem of core decomposition of a multilayer network. The multilayer context is much 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 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. 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 trades-off 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