Related papers: Susceptibility of random graphs with given vertex …
Components of complex systems are often classified according to the way they interact with each other. In graph theory such groups are known as clusters or communities. Many different techniques have been recently proposed to detect them,…
We study the following preferential attachment variant of the classical Erdos-Renyi random graph process. Starting with an empty graph on n vertices, new edges are added one-by-one, and each time an edge is chosen with probability roughly…
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 the problem of clustering grouped data with possibly non-exchangeable groups whose dependencies can be characterized by a known directed acyclic graph. To allow the sharing of clusters among the non-exchangeable groups, we…
We analyse the scaling limit of the sizes of the largest components of the Random Intersection Graph $G(n,m,p)$ close to the critical point $p=\frac{1}{\sqrt{nm}}$, when the numbers $n$ of individuals and $m$ of communities have different…
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…
In this paper we derive results concerning the connected components and the diameter of random graphs with an arbitrary i.i.d. degree sequence. We study these properties primarily, but not exclusively, when the tail of the degree…
Graph datasets are frequently constructed by a projection of a bipartite graph, where two nodes are connected in the projection if they share a common neighbor in the bipartite graph; for example, a coauthorship graph is a projection of an…
We study the asymptotic behaviour of the survival probability of a multitype branching process in random environment. The class of processes we consider here corresponds, in the one-dimensional situation, to the strongly subcritical case.…
An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…
For a given graph $H$, its subdivisions carry the same topological structure. The existence of $H$-subdivisions within a graph $G$ has deep connections with topological, structural and extremal properties of $G$. One prominent example of…
The finite-size scaling theory for continuous phase transition plays an important role in determining critical point and critical exponents from the size-dependent behaviors of quantities in the thermodynamic limit. For percolation phase…
We study cascading failures in smart grids, where an attacker selectively compromises the nodes with probabilities proportional to their degrees, betweenness, or clustering coefficient. This implies that nodes with high degrees,…
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
The maximum matching problem on random graphs is studied analytically by the cavity method of statistical physics. When the average vertex degree \mth{c} is larger than \mth{2.7183}, groups of max-matching patterns which differ greatly from…
We give a short proof that the largest component of the random graph $G(n, 1/n)$ is of size approximately $n^{2/3}$. The proof gives explicit bounds for the probability that the ratio is very large or very small.
We explore relations between various variational problems for graphs like Euler characteristic chi(G), characteristic length mu(G), mean clustering nu(G), inductive dimension iota(G), edge density epsilon(G), scale measure sigma(G), Hilbert…
A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrary positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the…
In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…
We determine the distributions of some random variables related to a simple model of an epidemic with contact tracing and cluster isolation. This enables us to apply general limit theorems for super-critical Crump-Mode-Jagers branching…