Related papers: Probabilistic Analysis of the Network Reliability …
The present study was concerned with network failure problems for simple connected undirected graphs. A connected graph becomes unconnected through edge failure, under the assumptions that only edges can fail and each edge has an identical…
In the present paper, we derive an upper bound of the average network breakdown probability of packet networks with unreliable relay nodes. We here assume that relay nodes get independently broken with a given node breakdown probability. A…
Graphs are fundamental mathematical structures used in various fields to model statistical and physical relationships between data, signals, and processes. In some applications, such as data processing in graphs that represent physical…
Connectivity of wireless sensor networks (WSNs) is a fundamental global property expected to be maintained even though some sensor nodes are at fault. In this paper, we investigate the connectivity of random geometric graphs (RGGs) in 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,…
Network reliability measures the probability that a target node is reachable from a source node in an uncertain graph, i.e., a graph where every edge is associated with a probability of existence. In this paper, we investigate the novel and…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
An $n$-tuple $D=(d(1),\dots,d(n))$ is a \emph{feasible degree sequence} if there is a graph on $\{1,\dots,n\}$ such that $i$ has degree $d(i)$. Any such graph will have $m=\sum_{i=1}^n d(i)/2$ edges. Letting $G(D)$ be a graph chosen…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
Desirable random graph models (RGMs) should (i) reproduce common patterns in real-world graphs (e.g., power-law degrees, small diameters, and high clustering), (ii) generate variable (i.e., not overly similar) graphs, and (iii) remain…
Designing reliable networks consists in finding topological structures, which are able to successfully carry out desired processes and operations. When this set of activities performed within a network are unknown and the only available…
A central concern of network operators is to estimate the probability of an incident that affects a significant part and thus may yield to a breakdown. We answer this question by modeling how a failure of either a node or an edge will…
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…
We consider the probability model of edge-fault tolerance of a network in the sense of connectivity with link faults. Using graph-theoretical notation, we define the edge-fault (EF) and Menger-type edge-fault (MEF) tolerances of a graph as…
We formalize the problem of detecting a community in a network into testing whether in a given (random) graph there is a subgraph that is unusually dense. We observe an undirected and unweighted graph on N nodes. Under the null hypothesis,…
The classic all-terminal network reliability problem posits a graph, each of whose edges fails independently with some given probability.
The network unreliability problem asks for the probability that a given undirected graph gets disconnected when every edge independently fails with a given probability $p$. Valiant (1979) showed that this problem is \#P-hard; therefore, the…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…