# Easily repairable networks: reconnecting nodes after damage

*Physical Review Letters* 113, 138701 (2014)

#resilience#graphtheory#infrastructure

Infrastructure networks can be vulnerable under attack. If we cannot protect them, how can we make them more repairable?

We introduce a simple class of distribution networks that withstand damage by being repairable instead of redundant. Instead of asking how hard it is to disconnect nodes through damage, we ask how easy it is to reconnect nodes after damage. We prove that optimal networks on regular lattices have an expected cost of reconnection proportional to the lattice length, and that such networks have exactly three levels of structural hierarchy. We extend our results to networks subject to repeated attacks, in which the repairs themselves must be repairable. We find that, in exchange for a modest increase in repair cost, such networks are able to withstand any number of attacks.

#### Snowflake-shaped networks are easiest to mend

Easily repairable networks: reconnecting nodes after damage

New Scientist, 2014-10-03

#### Snowflake Networks Make for the Best Tech

Easily repairable networks: reconnecting nodes after damage

Nature World News, 2014-10-04

#### A phase transition creates the geometry of the continuum from discrete space

R. Farr, T. Fink

Sub. to *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