Large-scale, highly-interconnected networks pervade our society and the natural world around us, including the World Wide Web, social networks, knowledge graphs, genome and scientific databases, medical and government records. The massive scale of graph data often surpasses the available computation and storage resources. Besides, users get overwhelmed by the daunting task of understanding and ...

An instance of the (r, p)-centroid problem is given by an edge and node weighted graph. Two competitors, the leader and the follower, are allowed to place p or r facilities, respectively, into the graph. Users at the nodes connect to the closest facility. A solution of the (r, p)-centroid problem is a leader placement such that the maximum total weight of the users connecting to any follower pl...

Annotation graph datasets are a natural representation of scientific knowledge. They are common in the life sciences where concepts such as genes and proteins are annotated with controlled vocabulary terms from ontologies. Scientists are interested in analyzing or mining these annotations, in synergy with the literature, to discover patterns. Further, annotated datasets provide an avenue for sc...

In this paper, we present a new approach towards a parallel resolution procedure which explores another dimension of parallelism in addition to the AND/OR formulation and special hardware constructs. The approach organizes the input clauses of a problem domain into a connection graph. The connection graph is then partitioned and each partition is worked on by a different processor of a multipro...

In bioinformatics, there exist multiple descriptions of graphs for the same set of genes or proteins. For instance, in yeast systems, graph edges can represent different relationships such as protein-protein interactions, genetic interactions, or co-participation in a protein complex, etc. Relying on similarities between nodes, each graph can be used independently for prediction of protein func...

Modularity allows to estimate the quality of a partition into communities of a graph composed of highly inter-connected vertices. In this article, we introduce a complementary measure, based on inertia, and specially conceived to evaluate the quality of a partition based on real attributes describing the vertices. We propose also I-Louvain, a graph nodes clustering method which uses our criteri...

a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

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in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

The main result of this article is a classification of distance-regular Cayley graphs on dihedral groups. There exist four obvious families of such graphs, which are called trivial. These are: complete graphs, complete bipartite graphs, complete bipartite graphs with the edges of a 1-factor removed, and cycles. It is proved that every nontrivial distance-regular Cayley graph on a dihedral group...