Related papers: Random graphs with arbitrary clustering and their …

In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…

Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…

Clustering and degree correlations are ubiquitous in real-world complex networks. Yet, understanding their role in critical phenomena remains a challenge for theoretical studies. Here, we provide the exact solution of site percolation in a…

Random networks are widely used to model complex networks and research their properties. In order to get a good approximation of complex networks encountered in various disciplines of science, the ability to tune various statistical…

Real-world networks often exhibit strong transitivity with nontrivial local clustering spectra and degree correlations. Such features are not easily modeled in tractable network models, creating an obstacle to the theoretical understanding…

Recent work on the internet, social networks, and the power grid has addressed the resilience of these networks to either random or targeted deletion of network nodes. Such deletions include, for example, the failure of internet routers or…

Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…

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…

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the Configuration Model where nodes of different types are connected via…

Percolation processes on random networks have been the subject of intense research activity over the last decades: the overall phenomenology of standard percolation on uncorrelated and unclustered topologies is well known. Still some…

Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…

The purpose of this paper is to analyze the degree index and clustering index in random graphs. The degree index in our setup is a certain measure of degree irregularity whose basic properties are well studied in the literature, and the…

Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…

The coexistence of sparsity and clustering (non-vanishing average fraction of triangles per node) is one of the few structural features that, irrespective of finer details, are ubiquitously observed across large real-world networks. This…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…

The random graph of Erdos and Renyi is one of the oldest and best studied models of a network, and possesses the considerable advantage of being exactly solvable for many of its average properties. However, as a model of real-world networks…

We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…

Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…