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The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
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 co-evolution between network structure and functional performance is a fundamental and challenging problem whose complexity emerges from the intrinsic interdependent nature of structure and function. Within this context, we investigate…
We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for…
We consider the time-dependent electron transport through a quantum dot coupled to two leads in the presence of the additional over-dot (bridge) tunneling channel. By using the evolution operator method together with the wide-band limit…
The analysis in this paper helps to explain the formation of growing networks with degree distributions that follow extended exponential or power-law tails. We present a generic model in which edge dynamics are driven by a continuous…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at…
We propose a general class of co-evolving tree network models driven by local exploration where new vertices attach to the current network via randomly sampling a vertex and then exploring the graph for a random number of steps in the…
We present exact results for the degree distribution in a directed network model that grows by node duplication (ND). Such models are useful in the study of the structure and growth dynamics of gene regulatory networks and scientific…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
For random walks on networks (graphs), it is a theoretical challenge to explicitly determine the mean first-passage time (MFPT) between two nodes averaged over all pairs. In this paper, we study the MFPT of random walks in the famous…
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…
Random walks have been proposed as a simple method of efficiently searching, or disseminating information throughout, communication and sensor networks. In nature, animals (such as ants) tend to follow correlated random walks, i.e., random…
Networks grow and evolve by local events, such as the addition of new nodes and links, or rewiring of links from one node to another. We show that depending on the frequency of these processes two topologically different networks can…
In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…
In this paper we derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the uniform multicommodity flow problem under random walk routing. We show the mean load is linearly dependent on the nodal…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…