Editing Spectral radius (section)

===Graphs===
The spectral radius of a finite [[Graph (discrete mathematics)|graph]] is defined to be the spectral radius of its [[adjacency matrix]].

This definition extends to the case of infinite graphs with bounded degrees of vertices (i.e. there exists some real number {{mvar|C}} such that the degree of every vertex of the graph is smaller than {{mvar|C}}). In this case, for the graph {{mvar|G}} define:

:<math> \ell^2(G) = \left \{ f : V(G) \to \mathbf{R} \ : \ \sum\nolimits_{v \in V(G)} \left \|f(v)^2 \right \| < \infty \right \}.</math>

Let {{mvar|γ}} be the adjacency operator of {{mvar|G}}:

:<math> \begin{cases} \gamma : \ell^2(G) \to \ell^2(G) \\ (\gamma f)(v) = \sum_{(u,v) \in E(G)} f(u) \end{cases}</math>

The spectral radius of {{mvar|G}} is defined to be the spectral radius of the bounded linear operator {{mvar|γ}}.