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A model for growing networks is introduced, having as a main ingredient that new nodes are attached to the network through one existing node and then explore the network through the links of the visited nodes. From exact calculations of two…
We study the inverse problem of determining the conductivity matrix of an electrical network from the prescribed knowledge of the magnitude of the induced current along the edges coupled with the imposed voltage or injected current on the…
We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…
We study a simple model in which the growth of a network is determined by the location of one or more random walkers. Depending on walker speed, the model generates a spectrum of structures situated between well-known limiting cases. We…
Random walks constitute a fundamental mechanism for a large set of dynamics taking place on networks. In this article, we study random walks on weighted networks with an arbitrary degree distribution, where the weight of an edge between two…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
We present a model for growing information networks where the ageing of a node depends on the time at which it entered the network and on the last time it was cited. The model is shown to undergo a transition from a small-world to…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
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…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
We present analytical results for the emerging structure of networks that evolve via a combination of growth (by node addition and random attachment) and contraction (by random node deletion). To this end we consider a network model in…
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of…
Confining an answer to the question whether and how the coherent operation of network elements is determined by the the network structure is the topic of our work. We map the structure of signal flow in directed networks by analysing the…
We introduce and simulate the random walk that adapts move strategies according to local node preferences on a directed graph. We consider graphs with double-hierarchical connectivity and variable wiring diagram in the universality class of…
In this paper, we investigate random walks in a family of small-world trees having an exponential degree distribution. First, we address a trapping problem, that is, a particular case of random walks with an immobile trap located at the…
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…
In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between…
We describe how noise propagates through a network by calculating the variance of the outputs. Using stochastic calculus and dynamical systems theory, we study the network topologies that accentuate or alleviate the effect of random…
We find that the simple coupling of network growth to the position of a random walker on the network generates a traveling wave in the probability distribution of nodes visited by the walker. We argue that the entropy of this probability…