Last Updated
：2025/12/04
Laplacian matrix
Noun
(graph
theory)
A
square
n⨯n
matrix
which
describes
an
undirected
graph
of
n
vertices
by
letting
rows
and
columns
correspond
to
vertices,
letting
its
diagonal
elements
contain
the
degrees
of
corresponding
vertices
and
letting
its
non-diagonal
elements
contain
either
−1
or
0
depending
on
whether
there
is
or
there
is
not
(respectively)
an
edge
connecting
the
pair
of
corresponding
vertices.
Japanese Meaning
無向グラフの各頂点を表すn個の行と列に対応し、対角成分には各頂点の次数（その頂点に接続する辺の数）が記録され、非対角成分には対応する頂点間に辺が存在する場合は−1、存在しない場合は0が記録される正方行列。
Sense（1）
(graph
theory)
A
square
n⨯n
matrix
which
describes
an
undirected
graph
of
n
vertices
by
letting
rows
and
columns
correspond
to
vertices,
letting
its
diagonal
elements
contain
the
degrees
of
corresponding
vertices
and
letting
its
non-diagonal
elements
contain
either
−1
or
0
depending
on
whether
there
is
or
there
is
not
(respectively)
an
edge
connecting
the
pair
of
corresponding
vertices.
（ plural ）
Quizzes for review
(graph theory) A square n⨯n matrix which describes an undirected graph of n vertices by letting rows and columns correspond to vertices, letting its diagonal elements contain the degrees of corresponding vertices and letting its non-diagonal elements contain either −1 or 0 depending on whether there is or there is not (respectively) an edge connecting the pair of corresponding vertices.
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See correct answer
Laplacian matrix
To determine the number of connected components in a network, one can analyze the multiplicity of the zero eigenvalue of the Laplacian matrix.
See correct answer
To determine the number of connected components in a network, one can analyze the multiplicity of the zero eigenvalue of the Laplacian matrix.
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