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In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
Percolation transition is widely observed in networks ranging from biology to engineering. While much attention has been paid to network topologies, studies rarely focus on critical percolation phenomena driven by network dynamics. Using…
A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
We introduce weighted Markovian graphs, a random walk model that decouples the transition dynamics of a Markov chain from (random) edge weights representing the cost of traversing each edge. This decoupling allows us to study the…
For realistic scale-free networks, we investigate the traffic properties of stochastic routing inspired by a zero-range process known in statistical physics. By parameters $\alpha$ and $\delta$, this model controls degree-dependent hopping…
This paper is concerned with the characterization of the relationship between topology and traffic dynamics. We use a model of network generation that allows the transition from random to scale free networks. Specifically, we consider three…
We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…
Most real-world networks are weighted graphs with the weight of the edges reflecting the relative importance of the connections. In this work, we study non degree dependent correlations between edge weights, generalizing thus the…
Many network analysis and graph learning techniques are based on models of random walks which require to infer transition matrices that formalize the underlying stochastic process in an observed graph. For weighted graphs, it is common to…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…
We study the tolerance to congestion failures in communication networks with scale-free topology. The traffic load carried by each damaged element in the network must be partly or totally redistributed among the remaining elements.…
Coherent transport of an excitation through a network corresponds to continuous-time quantum walk on a graph, and the transport properties of the system may be radically different depending on the graph and on the initial state. The…
A heterogeneous continuous time random walk is an analytical formalism for studying and modeling diffusion processes in heterogeneous structures on microscopic and macroscopic scales. In this paper we study both analytically and numerically…
In this study, we take a systematic look at the unrealised part of public transport networks (PTNs) with functional connections. We consider their complement graphs and study their structure. The complement graph $\bar G$ of an unweighted…
In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
In this letter, we propose a new routing strategy with a single free parameter $\alpha$ only based on local information of network topology. In order to maximize the packets handling capacity of underlying structure that can be measured by…
Complex numbers define the relationship between entities in many situations. A canonical example would be the off-diagonal terms in a Hamiltonian matrix in quantum physics. Recent years have seen an increasing interest to extend the tools…
A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended…