Related papers: Spanning Trees of Recursive Scale-Free Graphs
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
We discuss a category of graphs, recursive clique trees, which have small-world and scale-free properties and allow a fine tuning of the clustering and the power-law exponent of their discrete degree distribution. We determine relevant…
In this paper, we introduce two families of planar and self-similar graphs which have small-world properties. The constructed models are based on an iterative process where each step of a certain formulation of modules results in a final…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
In the present paper we consider the problem of constructing all the projective rooted spanning trees of a given graph. We propose an algorithm based on reducing this problem to the problem of constructing all the maximal independent sets…
We introduce and study the general problem of finding a most "scale-free-like" spanning tree of a connected graph. It is motivated by a particular problem in epidemiology, and may be useful in studies of various dynamical processes in…
We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical…
D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a…
We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…
Building on work by Desjarlais, Molina, Faase, and others, a general method is obtained for counting the number of spanning trees of graphs that are a product of an arbitrary graph and either a path or a cycle, of which grid graphs are a…
Message broadcasting in networks could be carried over spanning trees. A set of spanning trees in the same network is node independent if two conditions are satisfied. First, all trees are rooted at node $r$. Second, for every node $u$ in…
Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…
We discuss a recursive formula for number of spanning trees in a graph. The paper is written primary for school students.
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
We investigate a process of joining $k$ random spanning trees on a fixed clique $K_n$. The joined trees may not be disjoint and multiple edges are replaced by one simple edge. This process produces a simple graph $G$ on $n$~vertices with an…
In this paper we introduce a new model of random spanning trees that we call choice spanning trees, constructed from so-called choice random walks. These are random walks for which each step is chosen from a subset of random options,…
We give a proof for sharp estimate for the number of spanning trees using linear algebra and generalize this bound to multigraphs. In addition, we show that this bound is tight for complete graphs. In addition, we give estimates for number…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
Answering connectivity queries is fundamental to fully dynamic graphs where edges and vertices are inserted and deleted frequently. Existing work proposes data structures and algorithms with worst-case guarantees. We propose a new data…