相关论文: Random cherry graphs

Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even…

Net-trees are a general purpose data structure for metric data that have been used to solve a wide range of algorithmic problems. We give a simple randomized algorithm to construct net-trees on doubling metrics using $O(n\log n)$ time in…

Graph processes that unfold in continuous time are of obvious theoretical and practical interest. Particularly useful are those whose long-term behavior converges to a graph distribution of known form. Here, we review some of the conditions…

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes…

Exponential random graph models are a class of widely used exponential family models for social networks. The topological structure of an observed network is modelled by the relative prevalence of a set of local sub-graph configurations…

We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a…

We use the exponential random graph models to understand the network structure and its generative process for the Japanese bipartite network of banks and firms. One of the well known and simple model of exponential random graph is the…

The Ferrers bound conjecture is a natural graph-theoretic extension of the enumeration of spanning trees for Ferrers graphs. We document the current status of the conjecture and provide a further conjecture which implies it.

Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have…

Nowadays, exponential random graphs (ERGs) are among the most widely-studied network models. Different analytical and numerical techniques for ERG have been developed that resulted in the well-established theory with true predictive power.…

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…

In this work, which was inspired by the article [2] by M. V. Velasco and A. R. Villena, we obtain a characterization for probably continuous operators and show that the probability of a linear random operator being continuous coincides with…

We study spanning trees on Sierpinski graphs (i.e., finite approximations to the Sierpinski gasket) that are chosen uniformly at random. We construct a joint probability space for uniform spanning trees on every finite Sierpinski graph and…

Networks observed in the real world often have many short loops. This violates the tree-like assumption that underpins the majority of random graph models and most of the methods used for their analysis. In this paper we sketch possible…

We give alternate constructions of (i) the scaling limit of the uniform connected graphs with given fixed surplus, and (ii) the continuum random unicellular map (CRUM) of a given genus that start with a suitably tilted Brownian continuum…

Stochasticity is introduced to a well studied class of recursively grown graphs: $(u,v)$-flower nets, which have power-law degree distributions as well as small-world properties (when $u=1$). The stochastic variant interpolates between…

Inspired by [4] we present a new algorithm for uniformly random generation of ordered trees in which all occuring outdegrees can be specified by a given sequence of numbers. The method can be used for random generation of binary or n-ary…

The upper tail problem in a random graph asks to estimate the probability that the number of copies of some fixed subgraph in an Erd\H{o}s--R\'enyi random graph exceeds its expectation by some constant factor. There has been much exciting…

We study the influence of the seed in random trees grown according to the uniform attachment model, also known as uniform random recursive trees. We show that different seeds lead to different distributions of limiting trees from a total…