Related papers: Longest Path in the Price Model
In this work we consider a growing random graph sequence where a new vertex is less likely to join to an existing vertex with high degree and more likely to join to a vertex with low degree. In contrast to the well studied…
A graph generative model defines a distribution over graphs. One type of generative model is constructed by autoregressive neural networks, which sequentially add nodes and edges to generate a graph. However, the likelihood of a graph under…
Many networked systems involve multiple modes of transport. Such systems are called multimodal, and examples include logistic networks, biomedical phenomena, manufacturing process and telecommunication networks. Existing techniques for…
This paper proposes a new class of assortativity measures for weighted and directed networks. We extend the classical Newman's degree-degree assortativity by considering nodes' attributes different from the degree. Moreover, we propose…
Consider designing a transportation network on $n$ vertices in the plane, with traffic demand uniform over all source-destination pairs. Suppose the cost of a link of length $\ell$ and capacity $c$ scales as $\ell c^\beta$ for fixed…
The goal of this work is to model the peering arrangements between Autonomous Systems (ASes). Most existing models of the AS-graph assume an undirected graph. However, peering arrangements are mostly asymmetric Customer-Provider…
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model…
We present an analytical approach to calculating the distribution of shortest paths lengths (also called intervertex distances, or geodesic paths) between nodes in unweighted undirected networks. We obtain very accurate results for…
Constructions of directed configuration graphs based on a given bi-degree distribution were introduced in random graph theory some years ago. These constructions lead to graphs where the degrees of two nodes belonging to the same edge are…
Directed acyclic graphs (DAGs) are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical, as well as biological systems, where directed edges…
Given a directed acyclic graph with positive edge-weights, two vertices s and t, and a threshold-weight L, we present a fully-polynomial time approximation-scheme for the problem of counting the s-t paths of length at most L. We extend the…
We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and…
We examine adaptive strategies adopted by vehicles for route selection en-route in transportation networks. By studying a model of two-dimensional cellular automata, we model vehicles characterized by a parameter called path-greediness,…
In this paper, we consider the problem of reconstructing a directed graph using path queries. In this query model of learning, a graph is hidden from the learner, and the learner can access information about it with path queries. For a…
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…
A directed acyclic graph G = (V, E) is pseudo-transitive with respect to a given subset of edges E1, if for any edge ab in E1 and any edge bc in E, we have ac in E. We give algorithms for computing longest chains and demonstrate geometric…
Preferential attachment graphs are random graphs designed to mimic properties of typical real world networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already…
We study the growth of a directed network, in which the growth is constrained by the cost of adding links to the existing nodes. We propose a new preferential-attachment scheme, in which a new node attaches to an existing node i with…
Growing synthetic networks that follow power law distributions of a node's degree often involves adding one node at a time. Each node is added to the network with a fixed amount of edges and those edges are frozen for all future time steps.…
We study the problem of maximizing the number of spanning trees in a connected graph by adding at most $k$ edges from a given candidate edge set. We give both algorithmic and hardness results for this problem: - We give a greedy algorithm…