Related papers: Controlling the average degree in random power-law…
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…
In a graph, nodes can be characterized locally (with their degree $k$) or globally (e.g. with their average length path $\xi$ to other nodes). Here we investigate how $\xi$ depends on $k$. Our earlier algorithm of the construction of the…
We calculate the mean neighboring degree function $\bar k_{\rm{nn}}(k)$ and the mean clustering function $C(k)$ of vertices with degree $k$ as a function of $k$ in finite scale-free random networks through the static model. While both are…
We propose a simple dynamical model that generates networks with power-law degree distributions with the exponent 2 through rewiring only. At each time step, two nodes, i and j, are randomly selected, and one incoming link to i is…
Extensive studies have been done to understand the principles behind architectures of real networks. Recently, evidences for hierarchical organization in many real networks have also been reported. Here, we present a new hierarchical model…
Liu et al recently proposed a minimum number of driver nodes needed to obtain full structural controllability over a directed network. Driver nodes are unmatched nodes, from which there are directed paths to all matched nodes. Their most…
We investigate topologically biased failure in scale-free networks with degree distribution $P(k) \propto k^{-\gamma}$. The probability $p$ that an edge remains intact is assumed to depend on the degree $k$ of adjacent nodes $i$ and $j$…
Based on observations in the web-graph, the power-law hypothesis states that PageRank has a power-law distribution with the same exponent as the in-degree. While this hypothesis has been analytically verified for many random graph models,…
Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resultant disturbance in network properties is quintessential to understand real networks in action.…
We study the importance of local structural properties in networks which have been evolved for a power-law scaling in their Laplacian spectrum. To this end, the degree distribution, two-point degree correlations, and degree-dependent…
We study a simple model of dynamic networks, characterized by a set preferred degree, $\kappa$. Each node with degree $k$ attempts to maintain its $\kappa$ and will add (cut) a link with probability $w(k;\kappa)$ ($1-w(k;\kappa)$). As a…
The configuration model generates random graphs with any given degree distribution, and thus serves as a null model for scale-free networks with power-law degrees and unbounded degree fluctuations. For this setting, we study the local…
We propose a model that generates a new class of networks exhibiting power-law degree distribution with a spectrum of exponents depending on the number of links ($m$) with which incoming nodes join the existing network. Unlike the…
The resilience of a complex interconnected system concerns the size of the macroscopic functioning node clusters after external perturbations based on a random or designed scheme. For a representation of the interconnected systems with…
Degree correlation is a crucial measure in networks, significantly impacting network topology and dynamical behavior. The degree sequence of a network is a significant characteristic, and altering network degree correlation through…
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
Complex networks in different areas exhibit degree distributions with heavy upper tail. A preferential attachment mechanism in a growth process produces a graph with this feature. We herein investigate a variant of the simple preferential…
We introduce a general deterministic model for Apollonian Networks in an iterative fashion. The networks have small-world effect and scale-free topology. We calculate the exact results for the degree exponent, the clustering coefficient and…
In this paper we describe the emergence of scale-free degree distributions from statistical mechanics principles. We define an energy associated to a degree sequence as the logarithm of the number of indistinguishable simple networks it is…
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…