Abstract. In this paper we introduce graph-evolution rules, a novel type of frequency-based pattern that describe the evolution of large networks over time, at a local level. Given a sequence of snapshots of an evolving graph, we aim at discovering rules describing the local changes occurring in it. Adopting a definition of support based on minimum image we study the problem of extracting patterns whose frequency is larger than a minimum support threshold. Then, similar to the classical association rules framework, we derive graph-evolution rules from frequent patterns that satisfy a given minimum confidence constraint. We discuss merits and limits of alternative definitions of support and confidence, justifying the chosen framework. To evaluate our approach we devise GERM (Graph Evolution Rule Miner), an algorithm to mine all graph-evolution rules whose support and confidence are greater than given thresholds.The algorithm is applied to analyze four large real-world networks (i.e., two social networks, and two co-authorship networks from bibliographic data), using different time granularities. Our extensive experimentation confirms the feasibility and utility of the presented approach. It further shows that different kinds of networks exhibit different evolution rules, suggesting the usage of these local patterns to globally discriminate different kind of networks.
Abstract-Complex networks have been receiving increasing attention by the scientific community, thanks also to the increasing availability of real-world network data. In the last years, the multidimensional nature of many real world networks has been pointed out, i.e. many networks containing multiple connections between any pair of nodes have been analyzed. Despite the importance of analyzing this kind of networks was recognized by previous works, a complete framework for multidimensional network analysis is still missing. Such a framework would enable the analysts to study different phenomena, that can be either the generalization to the multidimensional setting of what happens in monodimensional network, or a new class of phenomena induced by the additional degree of complexity that multidimensionality provides in real networks. The aim of this paper is then to give the basis for multidimensional network analysis: we develop a solid repertoire of basic concepts and analytical measures, which takes into account the general structure of multidimensional networks. We tested our framework on a real world multidimensional network, showing the validity and the meaningfulness of the measures introduced, that are able to extract important, nonrandom, information about complex phenomena.
Abstract-Given a set of k networks, possibly with different sizes and no overlaps in nodes or links, how can we quickly assess similarity between them? Analogously, are there a set of social theories which, when represented by a small number of descriptive, numerical features, effectively serve as a "signature" for the network? Having such signatures will enable a wealth of graph mining and social network analysis tasks, including clustering, outlier detection, visualization, etc. We propose a novel, effective, and scalable method for solving the above problem. Our approach has the following desirable properties: (a) It is supported by a set of social theories. (b) It gives similarity scores that are sizeinvariant. (c) It is scalable, being linear on the number of links for graph signature extraction. We present extensive experiments on numerous synthetic and real networks from disparate domains, and show how we outperform baseline competitors. We also show how our approach enables several mining tasks such as clustering, visualization, discontinuity detection, network transfer learning, and re-identification across networks.
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