Related papers: Towards Modelling The Internet Topology - The Inte…
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…
The degree distributions of many real world networks follow power-laws whose exponents tend to fall between two and three. Within the framework of the Barabasi-Albert model (BA model), we explain this empirical observation by a simple fact.…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
The work presented in this thesis concerns different aspects of dynamical processes on networks. The first subject considered is the theoretical modeling of exploration processes of complex networks, such as the ``traceroute'' process used…
We present a link rewiring mechanism to produce surrogates of a network where both the degree distribution and the rich--club connectivity are preserved. We consider three real networks, the AS--Internet, the protein interaction and the…
Growing graphs describe a multitude of developing processes from maturing brains to expanding vocabularies to burgeoning public transit systems. Each of these growing processes likely adheres to proliferation rules that establish an…
The degree distribution of many biological and technological networks has been described as a power-law distribution. While the degree distribution does not capture all aspects of a network, it has often been suggested that its functional…
We consider a stochastic model for directed scale-free networks following power-laws in the degree distributions in both incoming and outgoing directions. In our model, the number of vertices grow geometrically with time with growth rate p.…
In search of many social and economical systems, it is found that node strength distribution as well as degree distribution demonstrate the behavior of power-law with droop-head and heavy-tail. We present a new model for the growth of…
Topology identification and inference of processes evolving over graphs arise in timely applications involving brain, transportation, financial, power, as well as social and information networks. This chapter provides an overview of graph…
Distribution grid is the medium and low voltage part of a large power system. Structurally, the majority of distribution networks operate radially, such that energized lines form a collection of trees, i.e. forest, with a substation being…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
On-line social networks, such as in Facebook and Twitter, are often studied from the perspective of friendship ties between agents in the network. Adversarial ties, however, also play an important role in the structure and function of…
We present here a study of the clustering and cycles in the graph of Internet at the Autonomous Systems level. We show that,even if the whole structure is changing with time, the statistical distributions of loops of order 3,4,5 remain…
Most real systems are growing. In order to model the evolution of real systems, many growing network models have been proposed to reproduce some specific topology properties. As the structure strongly influences the network function,…
Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to…
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…
Research on human online activities usually assumes that total activity $T$ increases linearly with active population $P$, that is, $T\propto P^{\gamma}(\gamma=1)$. However, we find examples of systems where total activity grows faster than…
Disease awareness in infection dynamics can be modeled with adaptive contact networks whose rewiring rules reflect the attempt by susceptibles to avoid infectious contacts. Simulations of this type of models show an active phase with…
In this work, we study the topological transition on the associated networks in a model proposed by Saeedian et al. (Scientific Reports 2019 9:9726), which considers a coupled dynamics of node and link states. Our goal was to better…