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The adjacency and degree functionalities that apply to simple graphs
(see Adjacency and Degree) similarly apply to multigraphs.
Given a vertex u of a graph G, return the degree of u, ie
the number of edges incident to u.
Given a multigraph G, and a non-negative integer n, return the set of
all vertices of G that have degree equal to n.
Maxdeg(G) : GrphMultUnd -> RngIntElt, GrphVert
The maximum of the degrees of the vertices of the multigraph G.
This function returns two values:
the maximum degree, and a vertex of G having
that degree.
Mindeg(G) : GrphMultUnd -> RngIntElt, GrphVert
The minimum of the degrees of the vertices of the multigraph G.
This function returns two values:
the minimum degree, and a vertex of G having
that degree.
Given a multigraph G such that the maximum degree of any vertex of G
is r, return a sequence D of length r + 1, such that D[i],
1 ≤i ≤r + 1, is the number of vertices in G having
degree i - 1.
Neighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of a graph G, return the set of vertices of
G that are adjacent to u.
Given a vertex u of a graph G, return the set of all edges
incident with the vertex u.
The number of edges directed into the vertex u belonging to a
multidigraph.
The number of edges of the form [u, v] where u is a vertex belonging
to a multidigraph.
Maxindeg(G) : GrphMultDir -> RngIntElt, GrphVert
The maximum indegree of the vertices of the multidigraph G.
This function returns two values: the maximum indegree,
and the first vertex of G having that degree.
Minindeg(G)) : GrphMultDir -> RngIntElt, GrphVert
The minimum indegree of the vertices of the multidigraph G.
This function returns two values: the minimum indegree,
and the first vertex of G having that degree.
Maxoutdeg(G) : GrphMultDir -> RngIntElt, GrphVert
The maximum outdegree of the vertices of the multidigraph G.
This function returns two values: the maximum outdegree,
and the first vertex of G having that degree.
Minoutdeg(G) : GrphMultDir -> RngIntElt, GrphVert
The minimum outdegree of the vertices of the multidigraph G.
This function returns two values: the minimum outdegree,
and the first vertex of G having that degree.
Given a vertex u belonging to the multidigraph G, return the total
degree of u, i.e. the sum of the in--degree and out--degree for u.
Maxdeg(G) : GrphMultDir -> RngIntElt, GrphVert
The maximum total degree of the vertices of the multidigraph G.
This function returns two values: the maximum total degree,
and the first vertex of G having that degree.
Mindeg(G) : GrphMultDir -> RngIntElt, GrphVert
The minimum total degree of the vertices of the multidigraph G.
This function returns two values: the minimum total degree,
and the first vertex of G having that degree.
Given a multidigraph G, and a non--negative integer n, return the set
of all vertices of G that have total degree equal to n.
Given a multidigraph G such that the maximum degree of any vertex of G
is r, return a sequence D of length r + 1, such that
D[i], 1 ≤i ≤r + 1,
is the number of vertices in G having degree i - 1.
InNeighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of a multidigraph G, return the set containing all
vertices v such that [v, u] is an edge in G, i.e. the initial
vertex of all edges that are directed into the vertex u.
OutNeighbors(u) : GrphVert -> { GrphVert }
Given a vertex u of the multidigraph G, return the set of vertices v
of G such that [u, v] is an edge in G, i.e. the set of
vertices v that are terminal vertices of edges directed from u to
v.
Given a vertex u of a graph G, return the set of all edges
incident with the vertex u, that is, the set of all edges incident
into u and incident from u.
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