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

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## Abstract

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## 1. Introduction

## 2. Percolation and Directed Percolation

## 3. Self-organized Criticality and the Fragment Method

## 4. Color-Avoiding Percolation

#### Site and Bond Color-Avoiding Percolation

- Independent colors: nodes can have at the same time more than one vulnerability/color;

## 5. Applications

## 6. Multilayer Model

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The phase diagram of the DK model, $\alpha $ marks the critical line separating the active and inactive (or absorbing) phase, $\gamma $ marks the “chaotic” phase near the corner $p=1,q=0$. The simplest mean-field approximation gives ${p}_{c}=1/2$ independently of q.

**Figure 2.**Phase planes of the bond CAP for two exclusive colors (denoted color 1 and 2). assigned to sites with probability $p(1)$ and $p(2)=1-p(1)$ and different dilutions (different connectivities).

**Figure 3.**Phase planes of the bond CAP for three exclusive colors, in networks with average connectivity $k=5$, at different values of the dilution parameter $\varphi $.

**Figure 4.**Phase planes of the bond CAP for three exclusive colors, with one trusted color with fixed probability $p(3)=0.2$, varying the average connectivity k of the network.

**Figure 5.**Phase space of directed percolation with interacting colors, case (a). The vertical axes is p and the horizontal one is q. For moderate values of $\epsilon $ one simply has a shift of the critical line, but for $\epsilon \ge 0.75$ a region near the corner $p=q=0$ becomes active.

**Figure 6.**Phase space of directed percolation with interacting colors, case (b). The vertical axes is p and the horizontal one is q. In this case, (disruptive interference among layers) the active region tends to occupy the whole line $p=0$.

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**MDPI and ACS Style**

Giusfredi, M.; Bagnoli, F. From Color-Avoiding to Color-Favored Percolation in Diluted Lattices. *Future Internet* **2020**, *12*, 139.
https://doi.org/10.3390/fi12080139

**AMA Style**

Giusfredi M, Bagnoli F. From Color-Avoiding to Color-Favored Percolation in Diluted Lattices. *Future Internet*. 2020; 12(8):139.
https://doi.org/10.3390/fi12080139

**Chicago/Turabian Style**

Giusfredi, Michele, and Franco Bagnoli. 2020. "From Color-Avoiding to Color-Favored Percolation in Diluted Lattices" *Future Internet* 12, no. 8: 139.
https://doi.org/10.3390/fi12080139