Related papers: Dynamics of directed graphs: the world-wide Web
We review recent results on the dynamics of social networks which suggest that the interplay between the network formation process and volatility may lead to the occurrence of discontinuous phase transitions and phase coexistence in a large…
Interdependent networks are characterized by two kinds of interactions: The usual connectivity links within each network and the dependency links coupling nodes of different networks. Due to the latter links such networks are known to…
We develop an agent-based model of strategic link formation in Research and Development (R&D) networks. Empirical evidence has shown that the growth of these networks is driven by mechanisms which are both endogenous to the system (that is,…
We present a comprehensive and versatile theoretical framework to study site and bond percolation on clustered and correlated random graphs. Our contribution can be summarized in three main points. (i) We introduce a set of iterative…
We study the synchronization of coupled dynamical systems on a variety of networks. The dynamics is governed by a local nonlinear map or flow for each node of the network and couplings connecting different nodes via the links of the…
A model of $s$ interacting species is considered with two types of dynamical variables. The fast variables are the populations of the species and slow variables the links of a directed graph that defines the catalytic interactions among…
Recently, statistical properties of the World-Wide Web have attracted considerable attention when self-similar regimes have been observed in the scaling of its link structure. Here we recall a classical model for general scaling phenomena…
Complex networks have non-trivial characteristics and appear in many real-world systems. Such networks are vitally important, but their full underlying dynamics are not completely understood. Utilizing new data sources, however, can unveil…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
We introduce a model for the dynamic self-organization of the electric grid. The model is characterized by a conserved magnitude, energy, that can travel following the links of the network to satisfy nodes' load. The load fluctuates in time…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…
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,…
Complex networks are used to depict topological features of complex systems. The structure of a network characterizes the interactions among elements of the system, and facilitates the study of many dynamical processes taking place on it.…
In this letter we present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze WWW data set and authorship collaboration networks in order to check the presence of correlation in the data.…
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…
This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach…
In this paper we introduce a novel description of the equilibrium state of a bond percolation process on random graphs using the exact method of generating functions. This allows us to find the expected size of the giant connected component…
In the context of growing networks, we introduce a simple dynamical model that unifies the generic features of real networks: scale-free distribution of degree and the small world effect. While the average shortest path length increases…
We propose a geometric model to quantify the dynamics of attention in online communities. Using clicks as a proxy of attention, we find that the diffusion of collective attention in Web forums and news sharing sites forms time-invariant…
We study the growth of random networks under a constraint that the diameter, defined as the average shortest path length between all nodes, remains approximately constant. We show that if the graph maintains the form of its degree…