Related papers: Funnelling effect in networks
We investigate the behavior of a threshold model for the spreading of fads and similar phenomena in society. The model is giving the fad dynamics and is intended to be confined to an underlying network structure. We investigate the whole…
We derive novel analytic tools for the discrete Bass model, which models the diffusion of new products on networks. We prove that the probability that any two nodes adopt by time t, is greater than or equal to the product of the…
The scaling behavior of fluctuation for a download network which we have investigated a few years ago based upon Zhang's Encophysics web page has been presented. A power law scaling, namely $\sigma \sim < f> ^ \alpha $ exists between the…
Many complex systems--from social and communication networks to biological networks and the Internet--are thought to exhibit scale-free structure. However, prevailing explanations rely on the constant addition of new nodes, an assumption…
Based on the formation of triad junctions, the proposed mechanism generates networks that exhibit extended rather than single power law behavior. Triad formation guarantees strong neighborhood clustering and community-level characteristics…
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 study the load distribution in weighted networks by measuring the effective number of optimal paths passing through a given vertex. The optimal path, along which the total cost is minimum, crucially depend on the cost distribution…
We characterize the distributions of size and duration of avalanches propagating in complex networks. By an avalanche we mean the sequence of events initiated by the externally stimulated `excitation' of a network node, which may, with some…
It has been discovered recently that many social, biological and ecological systems have the so-called small-world and scale-free features, which has provoked new research interest in the studies of various complex networks. Yet, most…
A discrete-time random process is described which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory…
We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their…
Kauffman net is a dynamical system of logical variables receiving two random inputs and each randomly assigned a boolean function. We show that the attractor and transient lengths exhibit scaleless behavior with power-law distributions over…
Using a steady state process of node duplication and deletion we produce networks with 1/k scale-free degree distributions in the limit of vanishing connectance. This occurs even though there is no growth involved and inherent preferential…
Localization phenomena permeate many branches of physics playing a fundamental role on dynamical processes evolving on heterogeneous networks. These localization analyses are frequently grounded, for example, on eigenvectors of adjacency or…
Milgram empirically showed that people knowing only connections to their friends could locate any person in the U.S. in a few steps. Later research showed that social network topology enables a node aware of its full routing to find an…
We introduce a growing network model---the copying model---in which a new node attaches to a randomly selected target node and, in addition, independently to each of the neighbors of the target with copying probability $p$. When…
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…
Percolation, the formation of a macroscopic connected component, is a key feature in the description of complex networks. The dynamical properties of a variety of systems can be understood in terms of percolation, including the robustness…
Preferential attachment is one possible way to obtain a scale-free network. We develop a self-consistent method to determine whether preferential attachment occurs during the growth of a network, and to extract the preferential attachment…
Power law distribution seems to be an important characteristic of web graphs. Several existing web graph models generate power law graphs by adding new vertices and non-uniform edge connectivities to existing graphs. Researchers have…