Degree Matrix
In the
mathematical
field of
graph theory
the
degree matrix
is a
diagonal matrix
which contains information about the
degree
of each
vertex
.
Definition
Given a graph
G=(V,E)
with
\|V\|=n
the
degree matrix
D
for
G
is a
n \times n
square matrix
defined as
d_{i,j}:=\left\{
\begin{matrix} \deg(v_i) & \mbox{if}\ i = j \\ 0 & \mbox{otherwise} \end{matrix} \right.
Examples
the diagonal matrix of a
k-regular graph
has a constant diagonal of
k
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