Related papers: Shortest path discovery of complex networks
In the field of computer science, the network reliability problem for evaluating the network failure probability has been extensively investigated. For a given undirected graph $G$, the network failure probability is the probability that…
1. The birth of network science. 2. What are random networks? 3. Adjacency matrix. 4. Degree distribution. 5. What are simple networks? Classical random graphs. 6. Birth of the giant component. 7. Topology of the Web. 8.Uncorrelated…
We describe a new method for the random sampling of connected networks with a specified degree sequence. We consider both the case of simple graphs and that of loopless multigraphs. The constraints of fixed degrees and of connectedness are…
Temporal networks have been increasingly used to model a diversity of systems that evolve in time; for example human contact structures over which dynamic processes such as epidemics take place. A fundamental aspect of real-life networks is…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…
In several important routing contexts it is required to identify a set of routes, each of which optimizes a different criterion. For instance, in the context of vehicle routing, one route would minimize the total distance traveled, while…
We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…
A very popular class of models for networks posits that each node is represented by a point in a continuous latent space, and that the probability of an edge between nodes is a decreasing function of the distance between them in this latent…
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…
We introduce a minimal model of small-world growing network generated by attaching to edges. The produced network is a plane graph which exists in real-life world. We obtain the analytic results of degree distribution decaying exponentially…
We analyze dynamic random network models where younger vertices connect to older ones with probabilities proportional to their degrees as well as a propensity kernel governed by their attribute types. Using stochastic approximation…
Consider a complete graph $K_n$ with edge weights drawn independently from a uniform distribution $U(0,1)$. The weight of the shortest (minimum-weight) path $P_1$ between two given vertices is known to be $\ln n / n$, asymptotically. Define…
Finding the shortest paths in road network is an important query in our life nowadays, and various index structures are constructed to speed up the query answering. However, these indexes can hardly work in real-life scenario because the…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
Network analysis has played a key role in knowledge discovery and data mining. In many real-world applications in recent years, we are interested in mining multilayer networks, where we have a number of edge sets called layers, which encode…
Network sampling is integral to the analysis of social, information, and biological networks. Since many real-world networks are massive in size, continuously evolving, and/or distributed in nature, the network structure is often sampled in…
We propose an extension of the Contextual Graph Markov Model, a deep and probabilistic machine learning model for graphs, to model the distribution of edge features. Our approach is architectural, as we introduce an additional Bayesian…
This work studies the limitations of uniquely identifying the structure (i.e., topology) of a networked linear system from partial measurements of its nodal dynamics. In general, many networks can be consistent with these measurements; this…
We consider the problem of extinction processes on random networks with a given structure. For sufficiently large well-mixed populations, the process of extinction of one or more state variable components occurs in the tail of the…