Related papers: From Graph Isoperimetric Inequality to Network Con…
A new metric for quantifying pairwise vertex connectivity in graphs is defined and an implementation presented. While general in nature, it features a combination of input features well-suited for social networks, including applicability to…
k-connectivity is an important measure of network robustness and resilience to random faults and disruptions. We undertake both local and global approaches to k-connectivity and calculate closed form analytic formulas for the probability…
Seeking effective neural networks is a critical and practical field in deep learning. Besides designing the depth, type of convolution, normalization, and nonlinearities, the topological connectivity of neural networks is also important.…
We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which…
We study a graph-theoretic property known as robustness, which plays a key role in certain classes of dynamics on networks (such as resilient consensus, contagion and bootstrap percolation). This property is stronger than other graph…
An edge-coloured graph $G$ is called $properly$ $connected$ if every two vertices are connected by a proper path. The $proper$ $connection$ $number$ of a connected graph $G$, denoted by $pc(G)$, is the smallest number of colours that are…
We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of…
This paper considers a kind of generalized measure $\lambda_s^{(h)}$ of fault tolerance in a hypercube-like graph $G_n$ which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes,…
We employ the mathematical programming approach in conjunction with the graph theory to study the structure of correspondent banking networks. Optimizing the network requires decisions to be made to onboard, terminate or restrict the bank…
In recent years, with the growing number of online social networks, these networks have become one of the best markets for advertising and commerce, so studying these networks is very important. Forecasting new edges in online social…
The algebraic connectivity of a network characterizes the lower-bound of the exponential convergence rate of consensus processes. This paper investigates the problem of accelerating the convergence of consensus processes by adding links to…
In this paper, the relationship between the network synchronizability and the edge distribution of its associated graph is investigated. First, it is shown that adding one edge to a cycle definitely decreases the network sychronizability.…
Network detection is an important capability in many areas of applied research in which data can be represented as a graph of entities and relationships. Oftentimes the object of interest is a relatively small subgraph in an enormous,…
The study of random graphs and networks had an explosive development in the last couple of decades. Meanwhile, techniques for the statistical analysis of sequences of networks were less developed. In this paper we focus on networks…
Random graphs are an important tool for modelling and analyzing the underlying properties of complex real-world networks. In this paper, we study a class of random graphs known as the inhomogeneous random K-out graphs which were recently…
The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such…
Whether as telecommunications or power systems, networks are very important in everyday life. Maintaining these networks properly functional and connected, even under attacks or failures, is of special concern. This topic has been…
Identifying networks with similar characteristics in a given ensemble, or detecting pattern discontinuities in a temporal sequence of networks, are two examples of tasks that require an effective metric capable of quantifying network…
Networks are useful for describing systems of interacting objects, where the nodes represent the objects and the edges represent the interactions between them. The applications include chemical and metabolic systems, food webs as well as…
Online social network services provide a platform for human social interactions. Nowadays, many kinds of online interactions generate large-scale social network data. Network analysis helps to mine knowledge and pattern from the…