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The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…
The characterization of the "most connected" nodes in static or slowly evolving complex networks has helped in understanding and predicting the behavior of social, biological, and technological networked systems, including their robustness…
We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional…
We introduce a new framework for the analysis of the dynamics of networks, based on randomly reinforced urn (RRU) processes, in which the weight of the edges is determined by a reinforcement mechanism. We rigorously explain the empirical…
Links in a practical network may have different functions, which makes the original network a combination of some functional subnetworks. Here, by a model of coupled oscillators, we investigate how such functional subnetworks are evolved…
Air transport systems are highly dynamic at temporal scales from minutes to years. This dynamic behavior not only characterizes the evolution of the system but also affect the system's functioning. Understanding the evolutionary mechanisms…
We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws to investigate the impact of transient dynamics caused by the rebalancing of loads after an initial network failure…
Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…
We propose a dynamical process for network evolution, aiming at explaining the emergence of the small world phenomenon, i.e., the statistical observation that any pair of individuals are linked by a short chain of acquaintances computable…
The study of network structural controllability focuses on the minimum number of driver nodes needed to control a whole network. Despite intensive studies on this topic, most of them consider static networks only. It is well-known, however,…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
What makes economic and ecological networks so unlike other highly skewed networks in their tendency toward turbulence and collapse? Here, we explore the consequences of a defining feature of these networks: their nodes are tied together by…
In this paper we study a model for traffic flow on networks based on a hyperbolic system of conservation laws with discontinuous flux. Each equation describes the density evolution of vehicles having a common path along the network. In this…
We provide a long-time existence and sub-convergence result for the elastic flow of a three network in $\mathbb{R}^{n}$ under some mild topological assumptions. The evolution is such that the sum of the elastic energies of the three curves…
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…
Algorithms for search of communities in networks usually consist discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a…
Transport networks, such as vasculature or river networks, provide key functions in organisms and the environment. They usually contain loops whose significance for the stability and robustness of the network is well documented. However,…
A number of important transport networks, such as the airline and trade networks of the world, exhibit a characteristic core-periphery structure, wherein a few nodes are highly interconnected and the rest of the network frays into a tree.…
If we add links to a network at random, a critical threshold can be crossed where a giant connected component forms. Conversely, if links or nodes are removed at random, the giant component shrinks and eventually breaks. In this paper, we…
In Nature, the primary goal of any network is to survive. This is less obvious for engineering networks (electric power, gas, water, transportation systems etc.) that are expected to operate under normal conditions most of time. As a…