num.edgesPEtri  R Documentation 
An object of class "NumEdges"
.
Returns the number of edges of
the underlying or reflexivity graph of
Proportional Edge Proximity Catch Digraphs (PEPCDs)
whose vertices are the
given 2D numerical data set, Xp
in a given triangle.
It also provides number of vertices
(i.e., number of data points inside the triangle)
and indices of the data points that reside in the triangle.
PE proximity region N_{PE}(x,r)
is defined
with respect to the triangle, tri
with expansion parameter r \ge 1
and vertex regions are
based on the center M=(m_1,m_2)
in Cartesian coordinates
or M=(\alpha,\beta,\gamma)
in barycentric coordinates
in the interior of the triangle tri
or
based on circumcenter of tri
;
default is M=(1,1,1)
,
i.e., the center of mass of tri
.
For the number of edges, loops are not allowed,
so edges are only possible for points
inside the triangle tri
for this function.
See also (\insertCiteceyhan:Phdthesis,ceyhan:stamet2016;textualpcds.ugraph).
num.edgesPEtri(
Xp,
tri,
r,
M = c(1, 1, 1),
ugraph = c("underlying", "reflexivity")
)
Xp 
A set of 2D points which constitute the vertices of PEPCD. 
tri 
A 
r 
A positive real number
which serves as the expansion parameter in PE proximity region;
must be 
M 
A 2D point in Cartesian coordinates
or a 3D point in barycentric coordinates
which serves as a center in the interior of the triangle 
ugraph 
The type of the graph based on PEPCDs,

A list
with the elements
desc 
A short description of the output: number of edges and quantities related to the triangle 
und.graph 
Type of the graph as "Underlying" or "Reflexivity" for the PEPCD 
num.edges 
Number of edges of the underlying
or reflexivity graphs based on the PEPCD
with vertices in the given triangle 
num.in.tri 
Number of 
ind.in.tri 
The vector of indices of the 
tess.points 
Tessellation points, i.e., points on which the tessellation of the study region is performed, here, tessellation is the support triangle. 
vertices 
Vertices of the underlying or reflexivity graph, 
Elvan Ceyhan
num.edgesPE
, num.edgesAStri
,
num.edgesCStri
, and num.arcsPEtri
#\donttest{
A<c(1,1); B<c(2,0); C<c(1.5,2);
Tr<rbind(A,B,C);
n<10
set.seed(1)
Xp<pcds::runif.tri(n,Tr)$g
M<as.numeric(pcds::runif.tri(1,Tr)$g)
Nedges = num.edgesPEtri(Xp,Tr,r=1.25,M)
Nedges
summary(Nedges)
plot(Nedges)
#}
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