Related papers: Dynamics of directed graphs: the world-wide Web
Random graphs have played an instrumental role in modelling real-world networks arising from the internet topology, social networks, or even protein-interaction networks within cells. Percolation, on the other hand, has been the fundamental…
We present a general class of geometric network growth mechanisms by homogeneous attachment in which the links created at a given time $t$ are distributed homogeneously between a new node and the exising nodes selected uniformly. This is…
We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model and, by performing percolation processes, we get information about topology and resilience properties of the networks…
We study the evolution of networks when the creation and decay of links are based on the position of nodes in the network measured by their centrality. We show that the same network dynamics arises under various centrality measures, and…
In many real, directed networks, the strongly connected component of nodes which are mutually reachable is very small. This does not fit with current theory, based on random graphs, according to which strong connectivity depends on mean…
Networks growing according to the rule that every new node has a probability p_k of being attached to k preexisting nodes, have a universal phase diagram and exhibit power law decays of the distribution of cluster sizes in the…
The description of the Internet topology is an important open problem, recently tackled with the introduction of scale-free networks. In this paper we focus on the topological and dynamical properties of real Internet maps in a three years…
In this paper we study the small-world network model of Watts and Strogatz, which mimics some aspects of the structure of networks of social interactions. We argue that there is one non-trivial length-scale in the model, analogous to the…
Measuring and optimizing the influence of nodes in big-data online social networks are important for many practical applications, such as the viral marketing and the adoption of new products. As the viral spreading on social network is a…
A minimal model for self-organized critical percolation on directed graphs with activating and de-activating links is studied. Unlike classical self-organized criticality, the variables that determine criticality are separated from the…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Networks in the real world do not exist as isolated entities, but they are often part of more complicated structures composed of many interconnected network layers. Recent studies have shown that such mutual dependence makes real networked…
We propose a growing network model for a community with a group structure. The community consists of individual members and groups, gatherings of members. The community grows as a new member is introduced by an existing member at each time…
It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated…
Traditional network generation models attempt to replicate global structural properties (degree distribution, average distance, clustering coefficient, communities, etc.) through synthetic link formation mechanisms such as triadic closure…
Human social behavior is organized in stratified, hierarchical networks, with a support group with about 5 members, expanding proportionally at each layer up to a maximum of approximately 150 frequent interactions per individual. This is…
Trends change rapidly in today's world, prompting this key question: What is the mechanism behind the emergence of new trends? By representing real-world dynamic systems as complex networks, the emergence of new trends can be symbolized by…
We investigate by random-walk simulations and a mean-field theory how growth by biased addition of nodes affects flow of the current through the emergent conducting graph, representing a digital circuit. In the interior of a large network…