Reactive random walkers on complex networks

Cencetti, Giulia; Battiston, Federico; Fanelli, Duccio; Latora, Vito

doi:10.1103/physreve.98.052302

Cited by 19 publications

(14 citation statements)

References 73 publications

(95 reference statements)

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“…This results in a flowing mechanism which asymptotically ends when all the nodes are equally populated. Such homogeneous state, where the concentration of agents is uniformly distributed, represents a stable equilibrium for the system, and, differently from related mobility processes such as random walks [9], does not depend on the structural features of the network. Nevertheless, the topology of the interactions has an important effect on the transient dynamics of the system, ultimately setting the time scale needed to reach the eventual equilibrium.…”

Section: Introductionmentioning

confidence: 98%

Diffusive behavior of multiplex networks

Cencetti

Battiston²

2019

New J. Phys.

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Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time scale of the multiplex to reach equilibrium is smaller than that of single networks in isolation, can emerge due to the interplay of these two mechanisms. In the limits of strong and weak inter-layer couplings multiplex diffusion has been linked to the spectrum of the supra-Laplacian associated to the system. However, a general theory for the emergence of this behavior is still lacking. Here we shed light on how the structural and dynamical features of the multiplex affect the Laplacian spectral properties. For instance, we find that super-diffusion emerges the earliest in systems with poorly diffusive layers, and that its onset is independent from the presence of overlap, which only influences the maximum relative intensity of the phenomenon. Moreover, a uniform allocation of resources to enhance diffusion within layers is preferable, as highly intra-layer heterogenous flows might hamper super-diffusion. Last, in multiplex networks formed by many layers, diffusion is best promoted by strengthening inter-layer flows across dissimilar layers. Our work can turn useful for the design of interconnected infrastructures in real-world transportation systems, clarifying the determinants able to drive the system towards the super-diffusive regime.

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Section: Introductionmentioning

confidence: 98%

Diffusive behavior of multiplex networks

Cencetti

Battiston²

2019

New J. Phys.

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“…Many variations of this fundamental process have since then been considered. These include more sophisticated dynamical implementations, which allow to targeting the walks towards nodes with given structural features [36], let them interact at the nodes of the network [37], investigate non-linear transition probabilities [38] and crowded conditions [39], consider the temporal [40][41][42] or multilayer [43,44] dimensions of the edges under different network topologies.…”

Section: Introductionmentioning

confidence: 99%

Random walks on hypergraphs

Battiston²,

et al. 2020

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In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but involve larger sets of nodes, at a time. These systems are thus better described in the framework of hypergraphs, whose hyperedges effectively account for multibody interactions. We hereby propose a new class of random walks defined on such higher-order structures, and grounded on a microscopic physical model where multi-body proximity is associated to highly probable exchanges among agents belonging to the same hyperedge. We provide an analytical characterisation of the process, deriving a general solution for the stationary distribution of the walkers. The dynamics is ultimately driven by a generalised random walk Laplace operator that reduces to the standard random walk Laplacian when all the hyperedges have size 2 and are thus meant to describe pairwise couplings. We illustrate our results on synthetic models for which we have a full control of the high-order structures, and real-world networks where higher-order interactions are at play. As a first application of the method, we compare the behaviour of random walkers on hypergraphs to that of traditional random walkers on the corresponding projected networks, drawing interesting conclusions on node rankings in collaboration networks. As a second application, we show how information derived from the random walk on hypergraphs can be successfully used for classification tasks involving objects with several features, each one represented by a hyperedge. Taken together, our work contributes to unveiling the effect of higher-order interactions on diffusive processes in higher-order networks, shading light on mechanisms at the hearth of biased information spreading in complex networked systems.

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“…Finally, more sophisticated discovery mechanisms could be included in the models. For example, explorers could interact in different ways with each other and with different items [138,139]. Alternatively, the exploration mechanism could rely on an intrinsic fitness for possible discoveries [140,141], and one could add a parameter controlling for the strength of the coupling to further investigate the relation between the coupling of the two networks and the distribution of item popularity [142].…”

Section: Perspective and Future Directionsmentioning

confidence: 99%

On the Dual Nature of Adoption Processes in Complex Networks

Iacopini

Latora

2021

Front. Phys.

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Adoption processes in socio-technological systems have been widely studied both empirically and theoretically. The way in which social norms, behaviors, and even items such as books, music, or other commercial or technological products spread in a population is usually modeled as a process of social contagion, in which the agents of a social system can infect their neighbors on the underlying network of social contacts. More recently, various models have also been proposed to reproduce the typical dynamics of a process of discovery, in which an agent explores a space of relations between ideas or items in search for novelties. In both types of processes, the structure of the underlying networks, respectively, the network of social contacts in the first case, and the network of relations among items in the second one, plays a fundamental role. However, the two processes have been traditionally seen and studied independently. Here, we provide a brief overview of the existing models of social spreading and exploration and of the latest advancements in both directions. We propose to look at them as two complementary aspects of the same adoption process: on the one hand, there are items spreading over a social network of individuals influencing each other, and on the other hand, individuals explore a network of similarities among items to adopt. The two-fold nature of the approach proposed opens up new stimulating challenges for the scientific community of network and data scientists. We conclude by outlining some possible directions that we believe may be relevant to be explored in the coming years.

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Reactive random walkers on complex networks

Cited by 19 publications

References 73 publications

Diffusive behavior of multiplex networks

Diffusive behavior of multiplex networks

Random walks on hypergraphs

On the Dual Nature of Adoption Processes in Complex Networks

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