Related papers: Local Leaders in Random Networks
We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…
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…
Complex networks across various fields are often considered to be scale free -- a statistical property usually solely characterized by a power-law distribution of the nodes' degree $k$. However, this characterization is incomplete. In…
Many complex networks are described by directed links; in such networks, a link represents, for example, the control of one node over the other node or unidirectional information flows. Some centrality measures are used to determine the…
A dynamical system is controllable if by imposing appropriate external signals on a subset of its nodes, it can be driven from any initial state to any desired state in finite time. Here we study the impact of various network…
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…
Recently, the first author showed that the giant in random undirected graphs is `almost' local. This means that, under a necessary and sufficient condition, the limiting proportion of vertices in the giant converges in probability to the…
We present a statistical mechanics approach for the description of complex networks. We first define an energy and an entropy associated to a degree distribution which have a geometrical interpretation. Next we evaluate the distribution…
We study the statistical properties of the sampled networks by a random walker. We compare topological properties of the sampled networks such as degree distribution, degree-degree correlation, and clustering coefficient with those of the…
A solution for the time- and age-dependent connectivity distribution of a growing random network is presented. The network is built by adding sites which link to earlier sites with a probability A_k which depends on the number of…
It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…
We focus on the role played by the node degree distribution on the way collective phenomena emerge on complex networks. To address this question, we focus analytically on a typical model for cooperative behaviour, the Majority Rule, applied…
We present a generator of random networks where both the degree-dependent clustering coefficient and the degree distribution are tunable. Following the same philosophy as in the configuration model, the degree distribution and the…
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…
In adversarial networks, edges correspond to negative interactions such as competition or dominance. We introduce a new type of node called a low-key leader in adversarial networks, distinguished by contrasting the centrality measures of…
We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s, for any…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
Systems which consist of many localized constituents interacting with each other can be represented by complex networks. Consistently, network science has become highly popular in vast fields focusing on natural, artificial and social…
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent…
The study of dynamical systems on networks, describing complex interactive processes, provides insight into how network structure affects global behaviour. Yet many methods for network dynamics fail to cope with large or partially-known…