Related papers: Scaling Properties of Paths on Graphs
We consider Markov logic networks and relational logistic regression as two fundamental representation formalisms in statistical relational artificial intelligence that use weighted formulas in their specification. However, Markov logic…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…
This paper provides an overview of results, concerning longest or heaviest paths, in the area of random directed graphs on the integers along with some extensions. We study first-order asymptotics of heaviest paths allowing weights both on…
Structural properties of evolving random graphs are investigated. Treating linking as a dynamic aggregation process, rate equations for the distribution of node to node distances (paths) and of cycles are formulated and solved analytically.…
We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…
The paper considers the behaviour of the number of paths of length $N$ on graphs with two heavy roots. Such vertices can be entropic traps. Numerical analysis is carried out for graphs with different degrees of root vertices. In the…
Duplication graphs are graphs that grow by duplication of existing vertices, and are important models of biological networks, including protein-protein interaction networks and gene regulatory networks. Three models of graph growth are…
The theory of dependency graphs is a powerful toolbox to prove asymptotic normality of sums of random variables. In this article, we introduce a more general notion of weighted dependency graphs and give normality criteria in this context.…
This paper develops a structural theory of unique shortest paths in real-weighted graphs. Our main goal is to characterize exactly which sets of node sequences, which we call path systems, can be realized as unique shortest paths in a graph…
A random graph evolution rule is considered. The graph evolution is based on interactions of three vertices. The weight of a clique is the number of its interactions. The asymptotic behaviour of the weights is described. It is known that…
We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
Accurately analyzing graph properties of social networks is a challenging task because of access limitations to the graph data. To address this challenge, several algorithms to obtain unbiased estimates of properties from few samples via a…
A random graph evolution based on the interactions of N vertices is studied. During the evolution both the preferential attachment method and the uniform choice of vertices are allowed. The weight of a vertex means the number of its…
A graphical model provides a compact and efficient representation of the association structure of a multivariate distribution by means of a graph. Relevant features of the distribution are represented by vertices, edges and other…
The aspect ratio of a (positively) weighted graph $G$ is the ratio of its maximum edge weight to its minimum edge weight. Aspect ratio commonly arises as a complexity measure in graph algorithms, especially related to the computation of…
We are interested in the asymptotic behavior of Markov chains on the set of positive integers for which, loosely speaking, large jumps are rare and occur at a rate that behaves like a negative power of the current state, and such that small…
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…
We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…