Topological perturbation of complex
networks
Perturbations in complex systems can deactivate some of the edges or
nodes.
Edge loss: the edge is deleted
Effects on the global topology:
Node loss: the node and all its edges are deleted
•
increase of path lengths,
• separation into isolated
clusters.
More connected
network -
less effect of an edge removal
But bridges are definite points of vulnerability!
The effect of a node removal depends on the number and
characteristics of its edges.

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Resilience to perturbations
Topological resilience studied in the literature:
the remaining nodes are still connected.
the average distance does not increase.
Ex Propose other measures of resilience
Ex. Propose other measures of resilience.
Testing resilience to incremental damage:
remove edges/nodes one by one, and look at
•
the size of the giant connected component
•
the average distance between nodes in the giant connected
component
Ex What factors affect the topological resilience of a network?
Ex. What factors affect the topological resilience of a network?