Related papers: The Clustering Coefficient of a Scale-Free Random …
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
We introduce a clustering coefficient for nondirected and directed hypergraphs, which we call the quad clustering coefficient. We determine the average quad clustering coefficient and its distribution in real-world hypergraphs and compare…
A permutation of [n] induces a graph on [n] such that the edges of the graph correspond to inversion pairs of the permutation. This graph is connected if and only if the corresponding permutation is indecomposable. Let s(n,m) denote a…
In this paper, a simply rule that generates scale-free networks with very large clustering coefficient and very small average distance is presented. These networks are called {\bf Multistage Random Growing Networks}(MRGN) as the adding…
Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their…
Motivated by the analysis of social networks, we study a model of random networks that has both a given degree distribution and a tunable clustering coefficient. We consider two types of growth processes on these graphs: diffusion and…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
We find precise asymptotic estimates for the number of planar maps and graphs with a condition on the minimum degree, and properties of random graphs from these classes. In particular we show that the size of the largest tree attached to…
We are interested in the probability that two randomly selected neighbors of a random vertex of degree (at least) $k$ are adjacent. We evaluate this probability for a power law random intersection graph, where each vertex is prescribed a…
We consider a random graph on a given degree sequence ${\cal D}$, satisfying certain conditions. We focus on two parameters $Q=Q({\cal D}), R=R({\cal D})$. Molloy and Reed proved that Q=0 is the threshold for the random graph to have a…
The triangle-free process begins with an empty graph on n vertices and iteratively adds edges chosen uniformly at random subject to the constraint that no triangle is formed. We determine the asymptotic number of edges in the maximal…
This article explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is…
We formulate a simple edge generation rule based on an inverse like mass action principle for random graphs over a structured vertex set. We show that under very weak assumptions on the structure generating distribution we obtain a scale…
Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its…
This paper presents an algorithm for generating scale-free networks with adjustable clustering coefficient. The algorithm is based on a random walk procedure combined with a triangle generation scheme which takes into account genetic…
In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last…
We prove that the class of chordal graphs is easily testable in the following sense. There exists a constant $c>0$ such that, if adding/removing at most $\epsilon n^2$ edges to a graph $G$ with $n$ vertices does not make it chordal, then a…
Probabilistic zero-forcing is a coloring process on a graph. In this process, an initial set of vertices is colored blue, and the remaining vertices are colored white. At each time step, blue vertices have a non-zero probability of forcing…
We study the synchronization transition in scale-free networks that display power-law asymptotic behaviors in their degree distributions. The critical coupling strength and the order-parameter critical exponent derived by the mean field…
The formation of triangles in complex networks is an important network property that has received tremendous attention. The formation of triangles is often studied through the clustering coefficient. The closure coefficient or transitivity…