The following diagrams illustrate fault tolerance in networks. Notice that the first one has many single points of failure, (a.k.a. SPOF).
In the second network, a break of any link or failure of any node will not impair the ability of nodes to communicate with one another.
The diagrams are clumped so as to demonstrate that nodes can be more or less well connected.
Example network - PGP web of trust
If we think of each node as a certifier of each connected node's
respective identity, then the destruction of any particular node
will not disrupt knowledge of others' identities.
Multiple paths through the web of trust strengthen's one's certainty of another's identity.