Related papers: Kinetic growth walks on complex networks
We study the problem of random search in finite networks with a tree topology, where it is expected that the distribution of the first-passage time F(t) decays exponentially. We show that the slope of the exponential tail is independent of…
We investigate network exploration by random walks defined via stationary and adaptive transition probabilities on large graphs. We derive an exact formula valid for arbitrary graphs and arbitrary walks with stationary transition…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
Efficient techniques to navigate networks with local information are fundamental to sample large-scale online social systems and to retrieve resources in peer-to-peer systems. Biased random walks, i.e. walks whose motion is biased on…
For a random walk on a network, the mean first-passage time from a node $i$ to another node $j$ chosen stochastically according to the equilibrium distribution of Markov chain representing the random walk is called Kemeny constant, which is…
Several interesting approaches have been reported in the literature on complex networks, random walks, and hierarchy of graphs. While many of these works perform random walks on stable, fixed networks, in the present work we address the…
Random graphs are a central element of the study of complex dynamical networks such as the internet, the brain, or socioeconomic phenomena. New methods to generate random graphs can spawn new applications and give insights into more…
The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in…
We study the detailed mechanism of the failure of scale-free networks under intentional attacks. Although it is generally accepted that such networks are very sensitive to targeted attacks, we show that for a particular type of structure…
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are…
Loops are subgraphs responsible for the multiplicity of paths going from one to another generic node in a given network. In this paper we present an analytic approach for the evaluation of the average number of loops in random scale-free…
Most real complex networks -- such as protein interactions, social contacts, the internet -- are only partially known and available to us. While the process of exploring such networks in many cases resembles a random walk, it becomes a key…
Ever since the Barab\'{a}si-Albert (BA) scale-free network has been proposed, network modeling has been studied intensively in light of the network growth and the preferential attachment (PA). However, numerous real systems are featured…
Network growth models that embody principles such as preferential attachment and local attachment rules have received much attention over the last decade. Among various approaches, random walks have been leveraged to capture such…
In this work, the outward and inward accessibilities of individual nodes are defined and their potential for application is illustrated with respect to the investigation of 6 different types of networks. The outward accessibility quantifies…
We introduce a deterministic model for scale-free networks, whose degree distribution follows a power-law with the exponent $\gamma$. At each time step, each vertex generates its offsprings, whose number is proportional to the degree of…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
Search patterns of randomly oriented steps of different lengths have been observed on all scales of the biological world, ranging from the microscopic to the ecological, including in protein motors, bacteria, T-cells, honeybees, marine…
We consider random walk and self-avoiding walk whose 1-step distribution is given by $D$, and oriented percolation whose bond-occupation probability is proportional to $D$. Suppose that $D(x)$ decays as $|x|^{-d-\alpha}$ with $\alpha>0$.…
We provide Monte Carlo estimates of the scaling of the length $L_{n}$ of the longest increasing subsequences of $n$-steps random walks for several different distributions of step lengths, short and heavy-tailed. Our simulations indicate…