Related papers: Sharpest possible clustering bounds using robust r…
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…
We derive the sampling properties of random networks based on weights whose pairwise products parameterize independent Bernoulli trials. This enables an understanding of many degree-based network models, in which the structure of realized…
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: (i) a dense…
We study the joint degree counts in proportional attachment random graphs and find a simple representation for the limit distribution in infinite sequence space. We show weak convergence with respect to the p-norm topology for appropriate p…
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…
Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial for understanding the function, performance and evolution of complex systems. In the last few…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a phase transition…
Network data sets are often constructed by some kind of thresholding procedure. The resulting networks frequently possess properties such as heavy-tailed degree distributions, clustering, large connected components and short average…
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…
We derive the finite size dependence of the clustering coefficient of scale-free random graphs generated by the configuration model with degree distribution exponent $2<\gamma<3$. Degree heterogeneity increases the presence of triangles in…
We performed a large-scale crawl of the World Wide Web, covering 6.9 Million domains and 57 Million subdomains, including all high-traffic sites of the Internet. We present a study of the correlations found between quantities measuring the…
A random intersection graph is constructed by assigning independently to each vertex a subset of a given set and drawing an edge between two vertices if and only if their respective subsets intersect. In this paper a model is developed in…
One of the main characteristics of real-world networks is their large clustering. Clustering is one aspect of a more general but much less studied structural organization of networks, i.e. edge multiplicity, defined as the number of…
It is commonly believed that scale-free networks are robust to massive numbers of random node deletions. For example, Cohen et al. study scale-free networks including some which approximate the measured degree distribution of the Internet.…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
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…
Sampling technique has become one of the recent research focuses in the graph-related fields. Most of the existing graph sampling algorithms tend to sample the high degree or low degree nodes in the complex networks because of the…
Data-driven analysis of complex networks has been in the focus of research for decades. An important area of research is to study how well real networks can be described with a small selection of metrics, furthermore how well network models…
Scale-free networks are characterized by a degree distribution with power-law behavior and have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks. Degree distributions of observed…