Related papers: Probabilistic Analysis of the Network Reliability …
Outage probabilities and single-hop throughput are two important performance metrics that have been evaluated for certain specific types of wireless networks. However, there is a lack of comprehensive results for larger classes of networks,…
In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…
We present and study the Static-Routing-Resiliency problem, motivated by routing on the Internet: Given a graph $G$, a unique destination vertex $d$, and an integer constant $c>0$, does there exist a static and destination-based routing…
In this paper we study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain so that it still contains a large (i.e. linear-sized) connected component…
We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
We propose the following model of a random graph on n vertices. Let F be a distribution in R_+^{n(n-1)/2} with a coordinate for every pair i$ with 1 \le i,j \le n. Then G_{F,p} is the distribution on graphs with n vertices obtained by…
This paper studies detecting anomalous edges in directed graphs that model social networks. We exploit edge exchangeability as a criterion for distinguishing anomalous edges from normal edges. Then we present an anomaly detector based on…
We study a generalization of the classical hidden clique problem to graphs with real-valued edge weights. Formally, we define a hypothesis testing problem. Under the null hypothesis, edges of a complete graph on $n$ vertices are associated…
Mapping the Internet generally consists in sampling the network from a limited set of sources by using traceroute-like probes. This methodology, akin to the merging of different spanning trees to a set of destination, has been argued to…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
Networks are known to be prone to link failures. In this paper we set out to investigate how networks of varying connectivity patterns respond to different link failure schemes in terms of connectivity, clustering coefficient and shortest…
Motivated by an application in community detection, we consider an \ER random graph conditioned on the rare event that all connected components are fully connected. Such graphs can be considered as partitions of vertices into cliques.…
We consider the problem of link prediction in networks whose edge structure may vary (sufficiently slowly) over time. This problem, with applications in many important areas including social networks, has two main variants: the first, known…
Large real-life complex networks are often modeled by various random graph constructions and hundreds of further references therein. In many cases it is not at all clear how the modeling strength of differently generated random graph model…
We provide new connectivity results for {\em vertex-random graphs} or {\em random annulus graphs} which are significant generalizations of random geometric graphs. Random geometric graphs (RGG) are one of the most basic models of random…
Current graph neural networks (GNNs) that tackle node classification on graphs tend to only focus on nodewise scores and are solely evaluated by nodewise metrics. This limits uncertainty estimation on graphs since nodewise marginals do not…