Random walks constitute a fundamental mechanism for large set of dynamics taking place on networks. In this article, we study random weighted networks with an arbitrary degree distribution, where the weight edge between two nodes has tunable parameter. By using spectral graph theory, derive analytical expressions stationary mean first-passage time (MFPT), average trapping (ATT), and lower bound ATT, which is defined as MFPT to given node over every starting point chosen from distribution....

The explicit determinations of the mean first-passage time (MFPT) for trapping problem are limited to some simple structure, e.g., regular lattices and geometrical fractals, determining MFPT random walks on other media, especially complex real networks, is a theoretical challenge. In this paper, we investigate walk pseudofractal scale-free web (PSFW) with perfect trap located at node highest degree, which simultaneously exhibits remarkable small-world properties observed in networks. We...

A vast variety of real-life networks display the ubiquitous presence scale-free phenomenon and small-world effect, both which play a significant role in dynamical processes running on networks. Although various have been investigated networks, analytical research about random walks such is much less. In this paper, we will study analytically scaling mean first-passage time (MFPT) for To end, first map classical Koch fractal to network, called network. According proposed mapping, present an...

In this paper, we propose a general framework for the trapping problem on weighted network with perfect trap fixed at an arbitrary node. By utilizing spectral graph theory, provide exact formula mean first-passage time (MFPT) from one node to another, based which deduce explicit expression average (ATT) in terms of eigenvalues and eigenvectors Laplacian matrix associated graph, where ATT is MFPTs over all source nodes. We then further derive sharp lower bound only local information node, can...

Many real networks share three generic properties: they are scale-free, display a small-world effect, and show power-law strength-degree correlation. In this paper, we propose type of deterministically growing called Sierpinski networks, which induced by the famous fractals constructed in simple iterative way. We derive analytical expressions for degree distribution, strength clustering coefficient, correlation, agree well with characterizations various real-life networks. Moreover, that...

The family of Vicsek fractals is one the most important and frequently studied regular fractal classes, it considerable interest to understand dynamical processes on this treelike family. In paper, we investigate discrete random walks fractals, with aim obtain exact solutions global mean-first-passage time (GMFPT), defined as average first-passage (FPT) between two nodes over whole fractals. Based known connections FPTs, effective resistance, eigenvalues graph Laplacian, determine implicitly...

Relatively general techniques for computing mean first-passage time (MFPT) of random walks on networks with a specific property are very useful since universal method calculating MFPT graphs is not available because their complexity and diversity. In this paper, we present explicitly determining the partial (PMFPT), i.e., average MFPTs to given target averaged over all possible starting positions, entire (EMFPT), which pairs nodes regular treelike fractals. We describe processes family...

Spanning trees are an important quantity characterizing the reliability of a network, however, explicitly determining number spanning in networks is theoretical challenge. In this paper, we study small-world scale-free network and obtain exact expressions. We find that entropy studied less than 1, which sharp contrast to previous result for regular lattice with same average degree, higher 1. Thus, much corresponding lattice. present difference lies disparate structure two networks. Since...

Spanning trees provide crucial insight into the origin of fractality in fractal scale-free networks. In this paper, we present number spanning a particular lattice (network). We first study analytically topological characteristics and show that it is simultaneously scale-free, highly clustered, "large-world," fractal, disassortative. Any previous model does not have all properties as studied one. Then, by using renormalization group technique derive network under consideration, based on...

Dendrimers and regular hyperbranched polymers are two classic families of macromolecules, which can be modeled by Cayley trees Vicsek fractals, respectively. In this paper, we study the trapping problem in fractals with different underlying geometries, focusing on a particular case perfect trap located at central node. For both networks, derive exact analytic formulas terms network size for average time (ATT)—the node-to-trap mean first-passage over whole networks. The obtained closed-form...

The vast majority of real-world networks are scale-free, loopy, and sparse, with a power-law degree distribution constant average degree. In this paper, we study first-order consensus dynamics in binary scale-free networks, where vertices subject to white noise. We focus on the coherence characterized terms H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm, which quantifies how closely agents track value. first provide lower bound...

We propose a simple algorithm which produces high dimensional Apollonian networks with both small-world and scale-free characteristics. derive analytical expressions for the degree distribution, clustering coefficient diameter of networks, are determined by their dimension.

The Vicsek fractals are one of the most interesting classes and study their structural properties is important. In this paper, exact formula for mean geodesic distance found. quantity computed precisely through recurrence relations derived from self-similar structure considered. obtained solution exhibits that approximately increases as an exponential function number nodes, with exponent equal to reciprocal fractal dimension. closed-form confirmed by extensive numerical calculations.

The determination of mean first-passage time (MFPT) for random walks in networks is a theoretical challenge, and topic considerable recent interest within the physics community. In this paper, according to known connections between MFPT, effective resistance, eigenvalues graph Laplacian, we first study analytically MFPT all node pairs class growing treelike networks, which term deterministic uniform recursive trees (DURTs), since one its particular cases version famous tree. interesting...