Related papers: Distribution of Edge Load in Scale-free Trees
Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs.…
We study localization of information on scale free networks with communication constraints when, for some reason, information can propagate only between ``mutually trusted nodes'' (MTN). We propose an algorithm to construct the MTN network…
We present a novel type of weighted scale-free network model, in which the weight grows independently of the attachment of new nodes. The evolution of this network is thus determined not only by the preferential attachment of new nodes to…
The concept of scale-free networks has been widely applied across natural and physical sciences. Many claims are made about the properties of these networks, even though the concept of scale-free is often vaguely defined. We present tools…
Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…
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 discuss several limiting degree distributions for a class of random threshold graphs in the many node regime. This analysis is carried out under a weak assumption on the distribution of the underlying fitness variable. This assumption,…
In a Bayesian network, we wish to evaluate the marginal probability of a query variable, which may be conditioned on the observed values of some evidence variables. Here we first present our "border algorithm," which converts a BN into a…
In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically…
Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining the number of spanning trees in networks is a theoretical challenge. In this paper, we study the number of spanning trees…
A weighted recursive tree is an evolving tree in which vertices are assigned random vertex-weights and new vertices connect to a predecessor with a probability proportional to its weight. Here, we study the maximum degree and near-maximum…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Complex networks are now being studied in a wide range of disciplines across science and technology. In this paper we propose a method by which one can probe the properties of experimentally obtained network data. Rather than just measuring…
In this paper, we study some important statistics of the random graph in the directed preferential attachment model introduced by B. Bollob\'as, C. Borgs, J. Chayes and O. Riordan. First, we find a new asymptotic formula for the expectation…
We prove polynomial upper and lower bounds on the expected size of the maximum agreement subtree of two random binary phylogenetic trees under both the uniform distribution and Yule-Harding distribution. This positively answers a question…
Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…
Complex network theory crucially depends on the assumptions made about the degree distribution, while fitting degree distributions to network data is challenging, in particular for scale-free networks with power-law degrees. We present a…
It has been found that the networks with scale-free distribution are very resilient to random failures. The purpose of this work is to determine the network design guideline which maximize the network robustness to random failures with the…
The time process of transport on randomly evolving trees is investigated. By introducing the notions of living and dead nodes a model of random tree evolution is constructed which describes the spreading in time of objects corresponding to…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…