Convolutional neural networks (CNNs) can be applied to graph similarity matching, in which case they are called graph CNNs. Graph CNNs are attracting increasing attention due to their effectiveness and efficiency. However, the existing convolution approaches focus only on regular data forms and require the transfer of the graph or key node neighborhoods of the graph into the same fixed form. Du...

A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it admits an orientation such that the out-neighborhood of every vertex is a clique in G. The class of 1-p.o. graphs forms a common generalization of the classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be recognized in polynomial time, no structural characterization of 1-p.o. graphs is known. In this ...

This paper describes a technique for reducing the querytime cost of HITS-like ranking algorithm. The basic idea is to compute for each node in the web graph a summary of its immediate neighborhood (which is a query-independent operation and thus can be done off-line), and to approximate the neighborhood graph of a result set at query-time by combining the summaries of the result set nodes. This...

Graph-based methods are very popular in semi-supervised learning due to their well founded theoretical background, intuitive interpretation of local neighborhood structure, and strong performance on a wide range of challenging learning problems. However, the success of these methods is highly dependent on the pre-existing neighborhood structure in the data used to construct the graph. In this p...

Define the neighborhood characteristic of a graph to be s1 − s2 + s3 − · · ·, where si counts subsets of i vertices that are all adjacent to some vertex outside the subset. This amounts to replacing cliques by neighborhoods in the traditional ‘Euler characteristic’ (the number of vertices, minus the number of edges, plus the number of triangles, etc.). The neighborhood characteristic can also b...

a {em 2-rainbow dominating function} (2rdf) of a graph $g$ is a function $f$ from the vertex set $v(g)$ to the set of all subsets of the set ${1,2}$ such that for any vertex $vin v(g)$ with $f(v)=emptyset$ the condition $bigcup_{uin n(v)}f(u)={1,2}$ is fulfilled, where $n(v)$ is the open neighborhood of $v$. the {em weight} of a 2rdf $f$ is the value $omega(f)=sum_{vin v}|f (v)|$. the {em $2$-r...

We consider neighborhood search defined on combinatorial optimization problems. Suppose that N is a Neighborhood for combinatorial optimization problem X. We say that N′ is LO-equivalent (locally optimal) to N if for any instance of X, the set of locally optimal solutions with respect to N and N′ are the same. The union of two LO-equivalent neighborhoods is itself LO-equivalent to the neighborh...

Schelling's classical segregation model gives a coherent explanation for the wide-spread phenomenon of residential segregation. We introduce an agent-based saturated open-city variant, Flip Schelling Process (FSP), in which agents, placed on graph, have one out two types and, based predominant type their neighborhood, decide whether to change types; similar new agent arriving as soon another le...

The p-competition graph G of a digraph D is a graph on the same vertex set as D, with x; y] 2 E(G) if and only if jOut(x) \Out(y)j p in D. In this paper we focus on the case in which D is a symmetric digraph ((a; b) is an arc in D if and only if (b; a) is an arc in D). We relate the problem to 2-step graphs, squares, and a generalization of the neighborhood graph called the p-neighborhood graph...

in this paper, we introduce the (g-$psi$) contraction in a metric space by using a graph.let $f,t$ be two multivalued mappings on $x.$ among other things, we obtain a common fixedpoint of the mappings $f,t$ in the metric space $x$ endowed with a graph $g.$