The.Algorithm.Design.Manual.Springer-Verlag.1998

The Friendship Graph
friendship graph would truly be the ultimate in social-ism.
● What is the largest clique?
A social clique is a group of mutual friends who all hang around together. A graph-theoretic
clique is a complete subgraph, where each vertex pair has an edge between them. Cliques are the
densest possible subgraphs. Within the friendship graph, we would expect to see large cliques
corresponding to workplaces, neighborhoods, religious organizations, and schools.
● How long will it take for my gossip to get back to me?
A cycle is a path where the last vertex is adjacent to the first. A cycle in which no vertex repeats
(such as 1-2-3-1 verus 1-2-3-2-1) is said to be simple. The shortest cycle in the graph defines the
graph's girth, while a simple cycle that passes through every vertex once is said to be a
Hamiltonian cycle. An undirected graph with no cycles is said to be a tree if it is connected;
otherwise it is a forest. A directed graph with no directed cycles is said to be a DAG, or directed
acyclic graph.
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Algorithms
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