Percolation and Internet Science

Bagnoli, Franco; Bellini, Emanuele; Massaro, Emanuele; Rechtman, Raúl

doi:10.3390/fi11020035

Cited by 7 publications

(2 citation statements)

References 116 publications

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“…It should be noted that percolation theory methods are widely used in various fields of science, not only in mathematics [21,22], physics [23,24] and computer science [25,26], descriptions of the spread of virus epidemics in networks [27,28], but also for example, in earth sciences [29][30][31], analysis of social network structures [32][33][34], and many others.…”

Section: Theoretical Methods Within Percolation Theorymentioning

confidence: 99%

The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

2019

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Analyses of the processes of information transfer within network structures shows that the conductivity and percolation threshold of the network depend not only on its density (average number of links per node), but also on its spatial symmetry groups and topological dimension. The results presented in this paper regarding conductivity simulation in network structures show that, for regular and random 2D and 3D networks, an increase in the number of links (density) per node reduces their percolation threshold value. At the same network density, the percolation threshold value is less for 3D than for 2D networks, whatever their structure and symmetry may be. Regardless of the type of networks and their symmetry, transition from 2D to 3D structures engenders a change of percolation threshold by a value exp{−(d − 1)} that is invariant for transition between structures, for any kind of network (d being topological dimension). It is observed that in 2D or 3D networks, which can be mutually transformed by deformation without breaking and forming new links, symmetry of similarity is observed, and the networks have the same percolation threshold. The presence of symmetry axes and corresponding number of symmetry planes in which they lie affects the percolation threshold value. For transition between orders of symmetry axes, in the presence of the corresponding planes of symmetry, an invariant exists which contributes to the percolation threshold value. Inversion centers also influence the value of the percolation threshold. Moreover, the greater the number of pairs of elements of the structure which have inversion, the more they contribute to the fraction of the percolation threshold in the presence of such a center of symmetry. However, if the center of symmetry lies in the plane of mirror symmetry separating the layers of the 3D structure, the mutual presence of this group of symmetry elements do not affect the percolation threshold value. The scientific novelty of the obtained results is that for different network structures, it was shown that the percolation threshold for the blocking of nodes problem could be represented as an additive set of invariant values, that is, as an algebraic sum, the value of the members of which is stored in the transition from one structure to another. The invariant values are network density, topological dimension, and some of the elements of symmetry (axes of symmetry and the corresponding number of symmetry planes in which they lie, centers of inversion).

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Section: Theoretical Methods Within Percolation Theorymentioning

confidence: 99%

The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

2019

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“…Percolation theory concerns the flow and the diffusion of some quantity on lattices or networks, for instance a disease on a human network or a message in a communication one [1][2][3]. It has many applications in the Internet science [4], for instance in the problem of robustness under attack [5], or the resilience after a random failure of nodes and/or links [6]. Classical percolation theory studies the penetration of a scalar quantity on a lattice, but it may be extended to more complex situations [7].…”

Section: Introductionmentioning

confidence: 99%

From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

Giusfredi

Bagnoli

2020

Future Internet

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We study the problem of color-avoiding and color-favored percolation in a network, i.e., the problem of finding a path that avoids a certain number of colors, associated with vulnerabilities of nodes or links, or is attracted by them. We investigate here regular (mainly directed) lattices with a fractions of links removed (hence the term “diluted”). We show that this problem can be formulated as a self-organized critical problem, in which the asymptotic phase space can be obtained in one simulation. The method is particularly effective for certain “convex” formulations, but can be extended to arbitrary problems using multi-bit coding. We obtain the phase diagram for some problem related to color-avoiding percolation on directed models. We also show that the interference among colors induces a paradoxical effect in which color-favored percolation is permitted where standard percolation for a single color is impossible.

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A Self-organized Criticality Method for the Study of Color-Avoiding Percolation

Giusfredi

Bagnoli

2019

Internet Science

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Percolation and Internet Science

Cited by 7 publications

References 116 publications

The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

The Influence of a Network’s Spatial Symmetry, Topological Dimension, and Density on Its Percolation Threshold

From Color-Avoiding to Color-Favored Percolation in Diluted Lattices

A Self-organized Criticality Method for the Study of Color-Avoiding Percolation

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