On fractionality of the path packing problem

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing each edge does not exceed 1. Well-known fractional path packing problem consists of maximizing the total weight of paths with ends in a subset S of TxT over all fractional multiflows. Together, G,T and S form a network. A network is an Eulerian network if all nodes in N\T have even degrees. A term "fractionality" was defined for the fractional path packing problem by A. Karzanov as the smallest natural number D so that there exists a solution to the problem that becomes integer-valued when multiplied by D. A. Karzanov has defined the class of Eulerian networks in terms of T and S, outside which D is infinite and proved that whithin this class D can be 1,2 or 4. He conjectured that D should be 1 or 2 for this class of networks. In this paper we prove this conjecture.Comment: 18 pages, 5 figures in .eps format, 2 latex files, main file is kc13.tex Resubmission due to incorrectly specified CS type of the article; no changes to the context have been mad

A.: Mining graph evolution rules

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.

An Efficiently Computable Support Measure for Frequent Subgraph Pattern Mining

Graph support measures are functions measuring how frequently a given subgraph pattern occurs in a given database graph. An important class of support measures relies on overlap graphs. A major advantage of the overlap graph based approaches is that they combine anti-monotonicity with counting occurrences of a pattern which are independent according to certain criteria. However, existing overlap graph based support measures are expensive to compute. In this paper, we propose a new support measure which is based on a new notion of independence. We show that our measure is the solution to a linear program which is usually sparse, and using interior point methods can be computed efficiently. We show experimentally that for large networks, in contrast to earlier overlap graph based proposals, pattern mining based on our support measure is feasible.status: publishe

Bipartite Graphs as Intermediate Model for RDF

Abstract. RDF Graphs are sets of assertions in the form of subjectpredicate-object triples of information resources. Although for simple examples they can be understood intuitively as directed labeled graphs, this representation does not scale well for more complex cases, particularly regarding the central notion of connectivity of resources. We argue in this paper that there is need for an intermediate representation of RDF to enable the application of well-established methods from graph theory. We introduce the concept of RDF Bipartite Graph triple syntax and data structures used by applications. In the light of this model we explore the issues of transformation costs, data/schemastructure, and the notion of RDF connectivity