<s>
In	O
the	O
mathematical	O
field	O
of	O
algebraic	O
graph	O
theory	O
,	O
the	O
degree	B-Algorithm
matrix	I-Algorithm
of	O
an	O
undirected	O
graph	O
is	O
a	O
diagonal	B-Algorithm
matrix	I-Algorithm
which	O
contains	O
information	O
about	O
the	O
degree	O
of	O
each	O
vertex	O
—	O
that	O
is	O
,	O
the	O
number	O
of	O
edges	O
attached	O
to	O
each	O
vertex	O
.	O
</s>
<s>
It	O
is	O
used	O
together	O
with	O
the	O
adjacency	B-Algorithm
matrix	I-Algorithm
to	O
construct	O
the	O
Laplacian	B-Algorithm
matrix	I-Algorithm
of	I-Algorithm
a	I-Algorithm
graph	I-Algorithm
:	O
the	O
Laplacian	B-Algorithm
matrix	I-Algorithm
is	O
the	O
difference	O
of	O
the	O
degree	B-Algorithm
matrix	I-Algorithm
and	O
the	O
adjacency	B-Algorithm
matrix	I-Algorithm
.	O
</s>
<s>
The	O
following	O
undirected	O
graph	O
has	O
a	O
6x6	O
degree	B-Algorithm
matrix	I-Algorithm
with	O
values	O
:	O
</s>
<s>
The	O
degree	B-Algorithm
matrix	I-Algorithm
of	O
a	O
k-regular	O
graph	O
has	O
a	O
constant	O
diagonal	O
of	O
.	O
</s>
<s>
According	O
to	O
the	O
degree	O
sum	O
formula	O
,	O
the	O
trace	O
of	O
the	O
degree	B-Algorithm
matrix	I-Algorithm
is	O
twice	O
the	O
number	O
of	O
edges	O
of	O
the	O
considered	O
graph	O
.	O
</s>
