Related papers: Kinetic growth walks on complex networks
The co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and…
We propose a consistent approach to the statistics of the shortest paths in random graphs with a given degree distribution. This approach goes further than a usual tree ansatz and rigorously accounts for loops in a network. We calculate the…
In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between…
In many complex systems, for the activity f(i) of the constituents or nodes i, a power-law relationship was discovered between the standard deviation sigma(i) and the average strength of the activity: sigma(i) ~ <f(i)>^alpha; universal…
We present an algorithm to grow a graph with scale-free structure of {\it in-} and {\it out-links} and variable wiring diagram in the class of the world-wide Web. We then explore the graph by intentional random walks using local…
Random walks process on networks plays a fundamental role in understanding the importance of nodes and the similarity of them, which has been widely applied in PageRank, information retrieval, and community detection, etc. Individual's…
The "power of choice" has been shown to radically alter the behavior of a number of randomized algorithms. Here we explore the effects of choice on models of tree and network growth. In our models each new node has k randomly chosen…
Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
We investigate hide-and-seek games on complex networks using a random walk framework. Specifically, we investigate the efficiency of various degree-biased random walk search strategies to locate items that are randomly hidden on a subset of…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
We study the properties of random walks on complex trees. We observe that the absence of loops reflects in physical observables showing large differences with respect to their looped counterparts. First, both the vertex discovery rate and…
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…
Scale-free power law structure describes complex networks derived from a wide range of real world processes. The extensive literature focuses almost exclusively on networks with power law exponent strictly larger than 2, which can be…
In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…
To study transport properties of complex networks, we analyze the equivalent conductance $G$ between two arbitrarily chosen nodes of random scale-free networks with degree distribution $P(k)\sim k^{-\lambda}$ in which each link has the same…
It was discovered a few years ago that many networks in the real world exhibit self-similarity. A lot of researches on the structures and processes on real and artificial fractal complex networks have been done, drawing an analogy to…
Random walk on discrete lattice models is important to understand various types of transport processes. The extreme events, defined as exceedences of the flux of walkers above a prescribed threshold, have been studied recently in the…