本文介绍了矩阵的谱半径定义及其在图论中的应用。对于任意复数矩阵A，其谱半径为所有特征值的最大模。此外，文中还讨论了有限图及其邻接矩阵的谱半径，并将其概念推广到具有有界顶点度的无限图。
Let λ1, ..., λn be the (real or complex) eigenvalues of a matrix A ∈ Cn×n. Then its spectral radius ρ(A) is defined as:
Graphs:
The spectral radius of a finite 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 C such that the degree of every vertex of the graph is smaller than C). In this case, for the graph G define:
Let γ be the adjacency operator of G:
The spectral radius of G is defined to be the spectral radius of the bounded linear operator γ.
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