# Self-healing networks: redundancy and structure

W. Quattrociocchi, G. Caldarelli, A. Scala

*PLOS ONE* 9, 87986 (2014)

#resilience#networktheory#infrastructure

Infrastructure networks are very well engineered systems characterized by fluxes of commodities, from electric power to drinking water.

We introduce the concept of self-healing in the field of complex networks. Obvious applications range from infrastructural to technological networks. By exploiting the presence of redundant links in recovering the connectivity of the system, we introduce self-healing capabilities through the application of distributed communication protocols granting the "smartness" of the system. We analyze the interplay between redundancies and smart reconfiguration protocols in improving the resilience of networked infrastructures to multiple failures; in particular, we measure the fraction of nodes still served for increasing levels of network damages. We study the effects of different connectivity patterns (planar square-grids, small-world, scale-free networks) on the healing performances. The study of small-world topologies shows us that the introduction of some long-range connections in the planar grids greatly enhances the resilience to multiple failures giving results comparable to the most resilient (but less realistic) scale-free structures.

#### Phase transition creates the geometry of the continuum from discrete space

R. Farr, T. Fink

*Physical Review E*

#### The statistical physics of real-world networks

G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli

*Nature Reviews Physics*

#### On defining the Hamiltonian beyond quantum theory

D. Branford, O. Dahlsten, A. Garner

*Foundations of Physics*

#### Reconstructing grain-shape statistics from electron back-scatter diffraction microscopy

R. Farr, Z. Vukmanovic, M. Holness, E. Griffiths

*Physical Review Materials*

#### Tackling information asymmetry in networks: a new entropy-based ranking index

P. Barucca, G. Caldarelli, T. Squartini

*Journal of Statistical Physics*

#### Eigenvalues of subgraphs of the cube

B. Bollobás, J. Lee, S. Letzter

*European Journal of Combinatorics*

#### Maximum one-shot dissipated work from Rényi divergences

N. Halpern, A. Garner, O. Dahlsten, V. Vedral

*Physical Review E *

123 / 123 papers