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We investigate the dynamics of a broad class of stochastic copying processes on a network that includes examples from population genetics (spatially-structured Wright-Fisher models), ecology (Hubbell-type models), linguistics (the utterance…
Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…
Communication of signals among nodes in a complex network poses fundamental problems of efficiency and cost. Routing of messages along shortest paths requires global information about the topology, while spreading by diffusion, which…
We propose that negative degree correlation among nodes in a network of nonlinear oscillators, often detected in real world networks, is motivated by its positive effects on synchronizability. In so doing, we use a novel methodology to…
We investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale-free neuronal networks with different average degrees and scaling exponents. As the…
The studies based on $A+A \rightarrow \emptyset$ and $A+B\rightarrow \emptyset$ diffusion-annihilation processes have so far been studied on weighted uncorrelated scale-free networks and fractal scale-free networks. In the previous reports,…
Many real-world scale-free networks, such as neural networks and online communication networks, consist of a fixed number of nodes but exhibit dynamic edge fluctuations. However, traditional models frequently overlook scenarios where the…
We introduce an exponential random graph model for networks with a fixed degree distribution and with a tunable degree-degree correlation. We then investigate the nature of a percolation transition in the correlated network with the Poisson…
We consider a discrete-time dynamical process on graphs, firstly introduced in connection with a protocol for controlling large networks of spin 1/2 quantum mechanical particles [Phys. Rev. Lett. 99, 100501 (2007)]. A description is as…
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…
In many networks such as transportation or communication networks, distance is certainly a relevant parameter. In addition, real-world examples suggest that when long-range links are existing, they usually connect to hubs-the well connected…
Complex networks are the subject of fundamental interest from the scientific community at large. Several metrics have been introduced to characterize the structure of these networks, such as the degree distribution, degree correlation, path…
We introduce a correlated static model and investigate a percolation transition. The model is a modification of the static model and is characterized by assortative degree-degree correlation. As one varies the edge density, the network…
Correlations may affect propagation processes on complex networks. To analyze their effect, it is useful to build ensembles of networks constrained to have a given value of a structural measure, such as the degree-degree correlation $r$,…
We consider a single-hop data gathering sensor cluster consisting of a set of sensors that need to transmit data periodically to a base-station. We are interested in maximizing the lifetime of this network. Even though the setting of our…
Nowadays there is a multitude of measures designed to capture different aspects of network structure. To be able to say if the structure of certain network is expected or not, one needs a reference model (null model). One frequently used…
A linear interference network is considered. Long-term fluctuations (shadow fading) in the wireless channel can lead to any link being erased with probability p. Each receiver is interested in one unique message that can be available at M…
We propose a model for growing networks based on a finite memory of the nodes. The model shows stylized features of real-world networks: power law distribution of degree, linear preferential attachment of new links and a negative…
The inverse problem of finding the optimal network structure for a specific type of dynamical process stands out as one of the most challenging problems in network science. Focusing on the susceptible-infected-susceptible type of dynamics…
We consider systems that are well modelled as a networks that evolve in time, which we call {\it Moving Neighborhood Networks}. These models are relevant in studying cooperative behavior of swarms and other phenomena where emergent…