Related papers: Roughness in Cayley Graphs
In this paper we study underlying graphs corresponding to a set of halving lines. We establish many properties of such graphs. In addition, we tighten the upper bound for the number of halving lines.
Random graphs have proven to be one of the most important and fruitful concepts in modern Combinatorics and Theoretical Computer Science. Besides being a fascinating study subject for their own sake, they serve as essential instruments in…
As an extension of positive or almost positive diagrams and links, we introduce a notion of successively almost positive diagrams and links, and good successively almost positive diagrams and links. We review various properties of positive…
Delaunay and Gabriel graphs are widely studied geometric proximity structures. Motivated by applications in wireless routing, relaxed versions of these graphs known as \emph{Locally Delaunay Graphs} ($LDGs$) and \emph{Locally Gabriel…
The emergence of massive graph data sets requires fast mining algorithms. Centrality measures to identify important vertices belong to the most popular analysis methods in graph mining. A measure that is gaining attention is forest…
In 2013, Jemal Abawajy, Andrei Kelarev and Morshed Chowdhury [1] proposed a problem to characterize the finite groups whose power graphs are Cayley graphs of some groups. Here we give a complete answer to this question.
We explore pseudometrics for directed graphs in order to better understand their topological properties. The directed flag complex associated to a directed graph provides a useful bridge between network science and topology. Indeed, it has…
Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…
The paper is a brief survey of some recent new results and progress of the Laplacian spectra of graphs and complex networks (in particular, random graph and the small world network). The main contents contain the spectral radius of the…
Introduced the quantitative measure of the structural complexity of the graph (complex network, etc.) based on a procedure similar to the renormalization process, considering the difference between actual and averaged graph structures on…
We study a modified notion of Ollivier's coarse Ricci curvature on graphs introduced by Lin, Lu, and Yau in [11]. We establish a rigidity theorem for complete graphs that shows a connected finite simple graph is complete if and only if the…
We study the k-median and k-center problems in probabilistic graphs. We analyze the hardness of these problems, and propose several algorithms with improved approximation ratios compared with the existing proposals.
Metric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes…
The relations, rather than the elements, constitute the structure of networks. We therefore develop a systematic approach to the analysis of networks, modelled as graphs or hypergraphs, that is based on structural properties of…
We study pseudo-geometric strongly regular graphs whose second subconstituent with respect to a vertex is a cover of a strongly regular graph or a complete graph. By studying the structure of such graphs, we characterize all graphs…
Robustness is a critical measure of the resilience of large networked systems, such as transportation and communication networks. Most prior works focus on the global robustness of a given graph at large, e.g., by measuring its overall…
This paper deals with some of the algebraic properties of Sierpi\'nski graphs and a family of regular generalized Sierpi\'nski graphs. For the family of regular generalized Sierpi\'nski graphs, we obtain their spectrum and characterize…
Cayley graph techniques are introduced for the problem of constructing networks having the maximum possible number of nodes, among networks that satisfy prescribed bounds on the parameters maximum node degree and broadcast diameter. The…
Mining graph data has become a popular research topic in computer science and has been widely studied in both academia and industry given the increasing amount of network data in the recent years. However, the huge amount of network data…
Graph neural networks are deep neural networks designed for graphs with attributes attached to nodes or edges. The number of research papers in the literature concerning these models is growing rapidly due to their impressive performance on…