Resilience is the ability of a system to withstand errors and attacks. In an electrical grid, for example, resilience would mean keeping power flowing when a transmission line or generator broke down. In traffic, it could mean the ability to reroute cars when a street is closed due to an accident.
Resilience is fundamentally a network property because it is usually achieved with redundant paths. When one path is no longer available, the others can still be used.
The simplest (and crudest) measure of resilience is the density of a network: the fraction of possible edges that exist. The more edges present in a network, the more redundant paths exist between its nodes. The following code uses the density() function to calculate this value for the example networks:
nx.density(G_karate)
0.13903743315508021
nx.density(G_karate)
0.011368341803124411
nx.density(G_karate...