Related papers: Transition from small to large world in growing ne…
The small-world transition is a first-order transition at zero density $p$ of shortcuts, whereby the normalized shortest-path distance undergoes a discontinuity in the thermodynamic limit. On finite systems the apparent transition is…
Networks of interconnected agents are essential to study complex networked systems' state evolution, stability, resilience, and control. Nevertheless, the high dimensionality and nonlinear dynamics are vital factors preventing us from…
We analyze an evolving network model of Krapivsky and Redner in which new nodes arrive sequentially, each connecting to a previously existing node b with probability proportional to the p-th power of the in-degree of b. We restrict to the…
We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a…
In this work, a growing network model that can generate a random network with finite degree in infinite time is studied. The dynamics are governed by a rule where the degree increases under a scheme similar to the Malthus-Verhulst model in…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
Real networks often grow through the sequential addition of new nodes that connect to older ones in the graph. However, many real systems evolve through the branching of fundamental units, whether those be scientific fields, countries, or…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many…
We use a simple dynamical model and explore coherent dynamics of wavepackets in complex networks of optical fibers. We start from a symmetric lattice and through the application of a Monte-Carlo criterion we introduce structural disorder…
We study growing networks in which each link carries a certain weight (randomly assigned at birth and fixed thereafter). The weight of a node is defined as the sum of the weights of the links attached to the node, and the network grows via…
Recurrence networks are complex networks, constructed from time series data, having several practical applications. Though their properties when constructed with the threshold value \epsilon chosen at or just above the percolation threshold…
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…
Networks are important representations in computer science to communicate structural aspects of a given system of interacting components. The evolution of a network has several topological properties that can provide us information on the…
Many real life networks, such as the World Wide Web, transportation systems, biological or social networks, achieve both a strong local clustering (nodes have many mutual neighbors) and a small diameter (maximum distance between any two…
We propose a natural model of evolving weighted networks in which new links are not necessarily connected to new nodes. The model allows a newly added link to connect directly two nodes already present in the network. This is plausible in…
Small-world (SW) networks have been identified in many different fields. Topological coefficients like the clustering coefficient and the characteristic path length have been used in the past for a qualitative characterization of these…
Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
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…