We consider the following problem: given a labelled directed graph G and a regular expression R, find all pairs of nodes connected by a simple path such that the concatenation of the labels along the path satisfies R. The problem is motivated by the observation that many recursive queries can be expressed in this form, and by the implementation of a query language, G+, based on this observation...

Analysing Web graphs has applications in determining page ranks, fighting Web spam, detecting communities and mirror sites, and more. This study is however hampered by the necessity of storing a major part of huge graphs in the external memory, which prevents efficient random access to edge (hyperlink) lists. A number of algorithm involving compression techniques have thus been presented, to re...

We describe a new technique for graph layout subject to constraints. Compared to previous techniques the proposed method is much faster and scalable to much larger graphs. For a graph with n nodes, m edges and c constraints it computes incremental layout in time O(n logn+m+ c) per iteration. Also, it supports a much more powerful class of constraint: inequalities or equalities over the Euclidea...

Graph searching is fundamental. Many graph algorithms employ some mechanism for systematically visiting all vertices and edges of a given graph. After choosing some initial sequence of vertices, it is natural to choose as the next vertex to visit some vertex that is adjacent to a previously visited vertex whenever possible. This statement describes graph search in its most general setting. When...

Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.

Let G = (V,E) be a simple graph with exactly n vertices and m edges. The aim of this paper is a new method for investigating nontriviality of the automorphism group of graphs. To do this, we prove that if |E| >=[(n - 1)2/2] then |Aut(G)|>1 and |Aut(G)| is even number.

let g be a simple graph. the hosoya polynomial of g is ( , ) ,( , ) = { , } ( ) xd u v h g x  u v v gwhere d(u,v) denotes the distance between vertices u and v . the dendrimer nanostar is apart of a new group of macromolecules. in this paper we compute the hosoya polynomial foran infinite family of dendrimer nanostar. as a consequence we obtain the wiener index andthe hyper-wiener index of th...

Based on the Belief Propagation Method, we propose simple and deterministic algorithms for some NP-hard graph partitioning problems, such as the Most Likely Partition problem and the Graph Bisection problem. These algorithms run in O(n+m) or O((n+m) log n) time on graphs with n vertices and m edges. For their average case analysis, we consider the planted solution model and prove that they yiel...

Batagelj and Zaversnik proposed a linear algorithm for the wellknown k-core decomposition problem. However, when k-cores are desired for a given k, we find that a simple linear algorithm requiring no sorting works for mining k-cores. In addition, this algorithm can be extended to mine (k1, k2, . . . , kp)-cores from p-partite graphs in linear time, and this mining approach can be efficiently im...

We investigate the problem of solving traditional combinatorial graph problems using secure multi-party computation techniques, focusing on the shortest path and the maximum flow problems. To the best of our knowledge, this is the first time these problems have been addressed in a general multi-party computation setting. Our study highlights several complexity gaps and suggests the exploration ...