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The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…
Traditional random graph models of networks generate networks that are locally tree-like, meaning that all local neighborhoods take the form of trees. In this respect such models are highly unrealistic, most real networks having strongly…
Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
Using the formalism of the biased random walk in random uncorrelated networks with arbitrary degree distributions, we develop theoretical approach to the critical packet generation rate in traffic based on routing strategy with local…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
Graphlets are induced subgraph patterns that are crucial to the understanding of the structure and function of a large network. A lot of efforts have been devoted to calculating graphlet statistics where random walk based approaches are…
We show how scale-free degree distributions can emerge naturally from growing networks by using random walks for selecting vertices for attachment. This result holds for several variants of the walk algorithm and for a wide range of…
The node2vec random walk has proven to be a key tool in network embedding algorithms. These random walks are tuneable, and their transition probabilities depend on the previous visited node and on the triangles containing the current and…
We address the question of understanding the effect of the underlying network topology on the spread of a virus and the dissemination of information when users are mobile performing independent random walks on a graph. To this end we…
We introduce a self-organized model of graph evolution associated with preferential network random walkers. The idea is developed by using two different types of walkers, the interactions of which lead to a dynamic graph. The walkers of the…
It was recently shown how graphs can be used to provide descriptions of psychopathologies, where symptoms of, say, depression, affect each other and certain configurations determine whether someone could fall into a sudden depression. To…
The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…
Random walks are the simplest way to explore or search a graph, and have revealed a very useful tool to investigate and characterize the structural properties of complex networks from the real world, e.g. they have been used to identify the…
A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time…
We propose an approximation for the first return time distribution of random walks on undirected networks. We combine a message-passing solution with a mean-field approximation, to account for the short- and long-term behaviours…
We consider the problem of determining the proportion of edges that are discovered in an Erdos-Renyi graph when one constructs all shortest paths from a given source node to all other nodes. This problem is equivalent to the one of…
We consider distributed networks, such as peer-to-peer networks, whose structure can be manipulated by adjusting the rules by which vertices enter and leave the network. We focus in particular on degree distributions and show that, with…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
Three models of growing random networks with fitness dependent growth rates are analysed using the rate equations for the distribution of their connectivities. In the first model (A), a network is built by connecting incoming nodes to nodes…