相关论文: Equal relation between the extra connectivity and …
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform…
In this paper we study the node failure identification problem in undirected graphs by means of Boolean Network Tomography. We argue that vertex connectivity plays a central role. We show tight bounds on the maximal identifiability in a…
This paper deals with dynamical networks for which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions…
The Ising model has become a popular psychometric model for analyzing item response data. The statistical inference of the Ising model is typically carried out via a pseudo-likelihood, as the standard likelihood approach suffers from a high…
Given a pair of graphs with the same number of vertices, the inexact graph matching problem consists in finding a correspondence between the vertices of these graphs that minimizes the total number of induced edge disagreements. We study…
The generalized $k$-connectivity of a graph $G$, denoted by $\kappa_k(G)$, is the minimum number of internally edge disjoint $S$-trees for any $S\subseteq V(G)$ and $|S|=k$. The generalized $k$-connectivity is a natural extension of the…
Networks and data supported on graphs have become ubiquitous in the sciences and engineering. This paper studies the 'blind' community detection problem, where we seek to infer the community structure of a graph model given the observation…
Current methods of graph signal processing rely heavily on the specific structure of the underlying network: the shift operator and the graph Fourier transform are both derived directly from a specific graph. In many cases, the network is…
These lecture notes are on automorphism groups of Cayley graphs and their applications to optimal fault-tolerance of some interconnection networks. We first give an introduction to automorphisms of graphs and an introduction to Cayley…
We find the asymptotic number of connected graphs with $k$ vertices and $k-1+l$ edges when $k,l$ approach infinity, reproving a result of Bender, Canfield and McKay. We use the {\em probabilistic method}, analyzing breadth-first search on…
The generalized connectivity of a graph $G$ was introduced by Chartrand et al. Let $S$ be a nonempty set of vertices of $G$, and $\kappa(S)$ be defined as the largest number of internally disjoint trees $T_1, T_2, \cdots, T_k$ connecting…
Recently, it has been proposed that the natural connectivity can be used to efficiently characterise the robustness of complex networks. Natural connectivity quantifies the redundancy of alternative routes in a network by evaluating the…
k-connectivity of random graphs is a fundamental property indicating reliability of multi-hop wireless sensor networks (WSN). WSNs comprising of sensor nodes with limited power resources are modeled by random graphs with unreliable nodes,…
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…
Neural networks, with powerful nonlinear mapping and classification capabilities, are widely applied in mechanical fault diagnosis to ensure safety. However, being typical black-box models, their application is limited in…
Identifying clusters of similar elements in a set is a common task in data analysis. With the immense growth of data and physical limitations on single processor speed, it is necessary to find efficient parallel algorithms for clustering…
A graph property is monotone if it is closed under removal of vertices and edges. In this paper we consider the following edge-deletion problem; given a monotone property P and a graph G, compute the smallest number of edge deletions that…
We conduct a systematic study of asynchronous models of distributed computing consisting of identical finite-state devices that cooperate in a network to decide if the network satisfies a given graph-theoretical property. Models discussed…
Networks are widely used to model the contact structure within a population and in the resulting models of disease spread. While networks provide a high degree of realism, the analysis of the exact model is out of reach and even numerical…
Random K-out graphs are used in several applications including modeling by sensor networks secured by the random pairwise key predistribution scheme, and payment channel networks. The random K-out graph with $n$ nodes is constructed as…