Grebinski and Kucherov (1998) and Alon et al. (2004-2005) study the problem of learning a hidden graph for some especial cases, such as hamiltonian cycle, cliques, stars, and matchings. This problem is motivated by problems in chemical reactions, molecular biology and genome sequencing. In this paper, we present a generalization of this problem. Precisely, we consider a graph G and a subgraph H...

We describe a test statistic based on the Lnorm of the eigenvectors of a modularity matrix to detect the presence of an embedded Erdős Rényi (ER) subgraph inside a larger ER random graph. An embedded subgraph may model a hidden community in a large network such as a social network or a computer network. We make use of the properties of the asymptotic distribution of eigenvectors of random graph...

We study the “subgraph connectivity” problem for undirected graphs with sublinear vertex update time. In this problem, we can make vertices active or inactive in a graph G, and answer the connectivity between two vertices in the subgraph of G induced by the active vertices. In this paper, we solve two open problems in subgraph connectivity. We give the first subgraph connectivity structure with...

Here, issues connected with characteristic stochastic practices are considered. In the first part, the plausibility of covering the arrangements of an improvement issue on subjective subgraphs is studied. The impulse for this strategy is a state where an advancement issue must be settled as often as possible for discretionary illustrations. Then, a preprocessing stage is considered that would q...

The growth of Big Data has seen the increasing prevalence of interconnected graph datasets that reflect the variety and complexity of emerging data sources. Recent distributed graph processing platforms offer vertex-centric and subgraphcentric abstractions to compose and execute graph analytics on commodity clusters and Clouds. Näıve translation of existing graph algorithms to these programming...

In the Maximum cost m′-subgraph problem we are given an undirected simple graph G(V,E) with weights w(v) on the vertices. The goal is to select a set U ⊆ V so that the number of edges with at least one endpoint in U is at most m′ with maximum weight W ∗. In [11] a ratio 3 approximation is given for problem. We improve this result by giving a 2 + approximation for the problem, for every constant...

Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within the traditional P vs NP dichotomy and within parameterized complexity. The Π-Subgraph problem asks whether an input graph contains an induced subgraph on at...

A large part of recent research on probabilistic and possibilistic inference networks has been devoted to learning them from data. In this paper we discuss two search methods and several evaluation measures usable for this task. We consider a scheme for evaluating induced networks and present experimental results obtained from an application of INES (Induction of NEtwork Structures), a prototyp...

Define a complete subgraph Q to be simplicial in a graph G when Q is contained in exactly one maximal complete subgraph (‘maxclique’) of G; otherwise, Q is nonsimplicial. Several graph classes—including strong p-Helly graphs and strongly chordal graphs—are shown to have pairs of peculiarly related new characterizations: (i) for every k ≥ 2, a certain property holds for the complete subgraphs th...

Let X, Y be connected graphs. A graph G is (X, Y )-free if G contains a copy of neither X nor Y as an induced subgraph. Pairs of connected graphs X, Y such that every 3-connected (X, Y )-free graph is Hamilton connected have been investigated most recently in [8] and [5]. This paper improves those results. Specifically, it is shown that every 3-connected (X, Y )-free graph is Hamilton connected...