Related papers: Scale-freeness under node removal: a finite-size s…
The rate equations are used to study the scale-free behavior of the weight distribution in evolving networks whose topology is determined only by degrees of preexisting vertices. An analysis of these equations shows that the degree…
Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their…
Many fibrous materials are modeled as elastic networks featuring a substantial separation between the stiffness scales that characterize different microscopic deformation modes of the network's constituents. This scale separation has been…
Analysis of degree-degree dependencies in complex networks, and their impact on processes on networks requires null models, i.e. models that generate uncorrelated scale-free networks. Most models to date however show structural negative…
Susceptibility of scale free Power Law (PL) networks to attacks has been traditionally studied in the context of what may be termed as {\em instantaneous attacks}, where a randomly selected set of nodes and edges are deleted while the…
Learning the network structure underlying data is an important problem in machine learning. This paper introduces a novel prior to study the inference of scale-free networks, which are widely used to model social and biological networks.…
It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in…
It has been well-known that many real networks are scale-free (SF) but extremely vulnerable against attacks. We investigate the robustness of connectivity and the lengths of the shortest loops in randomized SF networks with realistic…
We investigate the performance of linear consensus algorithms subject to a scaling of the underlying network size. Specifically, we model networked systems with $n^{\text{th}}$ order integrator dynamics over families of undirected, weighted…
Scale free dynamics are observed in a variety of physical and biological systems. These include neural activity in which evidence for scale freeness has been reported using a range of imaging modalities. Here, we derive the ways in which…
The existence of inter-dependence between multiple networks imparts an additional scale of complexity to such systems often referred to as `network of networks' (NON). We have investigated the robustness of NONs to random breakdown of their…
We propose a novel paradigm for modeling real-world scale-free networks, where the integration of new nodes is driven by the combined attractiveness of degree and betweenness centralities, the competition of which (expressed by a parameter…
Very often, when studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree-degree correlations are not present. However, simple constraints, such as the absence of multiple edges and…
Different weighted scale-free networks show weights-topology correlations indicated by the non linear scaling of the node strength with node connectivity. In this paper we show that networks with and without weight-topology correlations can…
A majority of studied models for scale-free networks have degree distributions with exponents greater than $2$. Real networks, however, can demonstrate essentially more heavy-tailed degree distributions. We explore two models of scale-free…
Probabilistic networks display a wide range of high average clustering coefficients independent of the number of nodes in the network. In particular, the local clustering coefficient decreases with the degree of the subtending node in a…
A thorough discussion of the statistical ensemble of scale-free connected random tree graphs is presented. Methods borrowed from field theory are used to define the ensemble and to study analytically its properties. The ensemble is…
We investigate the fundamental principles that drive the development of scalable algorithms for network optimization. Despite the significant amount of work on parallel and decentralized algorithms in the optimization community, the methods…
Recently, the concept of geometric renormalization group provides a good approach for studying the structural symmetry and functional invariance of complex networks. Along this line, we systematically investigate the finite-size scaling of…
This paper studies the robustness of large-scale interconnected systems with respect to external disturbances, focussing on their scalability properties. Specifically, a notion of scalability is introduced that asks for these robustness…