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For a finite graph $G$ on $n$ vertices, its graph bandwidth is the minimum of ${\max }_{uv\in E}|\ell (u)-\ell (v)|$ over all bijective labels $\ell :V\to \{1,\dots ,n\}$. It asks how close adjacent vertices can be placed in a line. For an edgeless graph the bandwidth is taken as zero.

A path has bandwidth one, while a complete graph has bandwidth $n-1$. With the same ordering of rows and columns, this is the smallest matrix bandwidth achievable for the adjacency matrix. It matters in storing sparse matrices and reducing the work or memory associated with interactions far from the diagonal.