Related papers: Are Barabasi-Albert networks self-averaging?
This paper mainly discusses the diffusion on complex networks with time-varying couplings. We propose a model to describe the adaptive diffusion process of local topological and dynamical information, and find that the Barabasi-Albert…
Higher order clustering coefficients $C(x)$ are introduced for random networks. The coefficients express probabilities that the shortest distance between any two nearest neighbours of a certain vertex $i$ equals $x$, when one neglects all…
The extreme eigenvalues of adjacency matrices are important indicators on the influences of topological structures to collective dynamical behavior of complex networks. Recent findings on the ensemble averageability of the extreme…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
We study the evolution of a random weighted network with complex nonlinear dynamics at each node, whose activity may cease as a result of interactions with other nodes. Starting from a knowledge of the micro-level behaviour at each node, we…
There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized,…
The epidemic curve and the final extent of the COVID-19 pandemic are usually predicted from the rate of early exponential raising using the SIR model. These predictions implicitly assume a full social mixing, which is not plausible…
It has previously been shown that the network of connected minima on a potential energy landscape is scale-free, and that this reflects a power-law distribution for the areas of the basins of attraction surrounding the minima. Here, we set…
Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment},…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Systems as diverse as genetic networks or the world wide web are best described as networks with complex topology. A common property of many large networks is that the vertex connectivities follow a scale-free power-law distribution. This…
The properties of the galaxy distribution at large scales are usually studied using statistics which are assumed to be self-averaging inside a given sample. We present a new analysis able to quantitatively map galaxy large scale structures…
Contrary to many recent models of growing networks, we present a model with fixed number of nodes and links, where it is introduced a dynamics favoring the formation of links between nodes with degree of connectivity as different as…
The network properties of a graph ensemble subject to the constraints imposed by the expected degree sequence are studied. It is found that the linear preferential attachment is a fundamental rule, as it keeps the maximal entropy in sparse…
The width of a neural network matters since increasing the width will necessarily increase the model capacity. However, the performance of a network does not improve linearly with the width and soon gets saturated. In this case, we argue…
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…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…
We study the evolution of a random graph under the constraint that the diameter remain constant as the graph grows. We show that if the graph maintains the form of its link distribution it must be scale-free with exponent between 2 and 3.…
The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and…