 
Summary: Topological perturbation of complex
networks
Effects on the global topology:
ˇ increase of path lengths,
ˇ 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.
Perturbations in complex systems can deactivate some of the edges or
nodes.
Edge loss: the edge is deleted
Node loss: the node and all its edges are deleted
Resilience to perturbations
Topological resilience: the remaining nodes are still connected.
the average distance does not increase.
We will remove edges/nodes one by one, and look at
ˇ the size of the giant connected component
ˇ the average distance between nodes in the giant connected
