Cohesive subgraph identification in large graphs

Graph data is ubiquitous in real world applications, as the relationship among entities in the applications can be naturally captured by the graph model. Finding cohesive subgraphs is a fundamental problem in graph mining with diverse applications. Given the important roles of cohesive subgraphs, this thesis focuses on cohesive subgraph identification in large graphs. Firstly, we study the size-bounded community search problem that aims to find a subgraph with the largest min-degree among all connected subgraphs that contain the query vertex q and have at least l and at most h vertices, where q, l, h are specified by the query. As the problem is NP-hard, we propose a branch-reduce-and-bound algorithm SC-BRB by developing nontrivial reducing techniques, upper bounding techniques, and branching techniques. Secondly, we formulate the notion of similar-biclique in bipartite graphs which is a special kind of biclique where all vertices from a designated side are similar to each other, and aim to enumerate all maximal similar-bicliques. We propose a backtracking algorithm MSBE to directly enumerate maximal similar-bicliques, and power it by vertex reduction and optimization techniques. In addition, we design a novel index structure to speed up a time-critical operation of MSBE, as well as to speed up vertex reduction. Efficient index construction algorithms are developed. Thirdly, we consider balanced cliques in signed graphs --- a clique is balanced if its vertex set can be partitioned into CL and CR such that all negative edges are between CL and CR --- and study the problem of maximum balanced clique computation. We propose techniques to transform the maximum balanced clique problem over G to a series of maximum dichromatic clique problems over small subgraphs of G. The transformation not only removes edge signs but also sparsifies the edge set

Métrologie des graphes de terrain, application à la construction de ressources lexicales et à la recherche d'information

This thesis is organized in two parts : the first part focuses on measures of similarity (or proximity) between vertices of a graph, the second part on clustering methods for bipartite graph. A new measure of similarity between vertices, based on short time random walks, is introduced. The main advantage of the method is that it is insensitive to the density of the graph. A broad state of the art of similarities between vertices is then proposed, as well as experimental comparisons of these measures. This is followed by the proposal of a robust method for comparing graphs sharing the same set of vertices. This measure is shown to be applicable to the comparison and merging of synonymy networks. Finally an application for the enrichment of lexical resources is presented. It consists in providing candidate synonyms on the basis of already existing links. In the second part, a parallel between formal concept analysis and clustering of bipartite graph is established. This parallel leads to the particular case where a partition of one of the vertex groups can be determined whereas there is no corresponding partition on the other group of vertices. A simple method that addresses this problem is proposed and evaluated. Finally, a system of automatic classification of search results (Kodex) is presented. This system is an application of previously seen clustering methods. An evaluation on a collection of two million web pages shows the benefits of the approach and also helps to understand some differences between clustering methods.Cette thèse s'organise en deux parties : une première partie s'intéresse aux mesures de similarité (ou de proximité) définies entre les sommets d'un graphe, une seconde aux méthodes de clustering de graphe biparti. Une nouvelle mesure de similarité entre sommets basée sur des marches aléatoires en temps courts est introduite. Cette méthode a l'avantage, en particulier, d'être insensible à la densité du graphe. Il est ensuite proposé un large état de l'art des similarités entre sommets, ainsi qu'une comparaison expérimentale de ces différentes mesures. Cette première partie se poursuit par la proposition d'une méthode robuste de comparaison de graphes partageant le même ensemble de sommets. Cette méthode est mise en application pour comparer et fusionner des graphes de synonymie. Enfin une application d'aide à la construction de ressources lexicales est présentée. Elle consiste à proposer de nouvelles relations de synonymie à partir de l'ensemble des relations de synonymie déjà existantes. Dans une seconde partie, un parallèle entre l'analyse formelle de concepts et le clustering de graphe biparti est établi. Ce parallèle conduit à l'étude d'un cas particulier pour lequel une partition d'un des groupes de sommets d'un graphe biparti peut-être déterminée alors qu'il n'existe pas de partitionnement correspondant sur l'autre type de sommets. Une méthode simple qui répond à ce problème est proposée et évaluée. Enfin Kodex, un système de classification automatique des résultats d'une recherche d'information est présenté. Ce système est une application en RI des méthodes de clustering vues précédemment. Une évaluation sur une collection de deux millions de pages web montre les avantages de l'approche et permet en outre de mieux comprendre certaines différences entre méthodes de clustering

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum