Returns \(I(p_2\) in \(N_{CS}(p_1,t,c))\) for points \(p_1\) and \(p_2\), that is, returns 1 if \(p_2\) is in \(N_{CS}(p_1,t,c)\), returns 0 otherwise, where \(N_{CS}(x,t,c)\) is the CS proximity region for point \(x\) with expansion parameter \(t>0\) and centrality parameter \(c \in (0,1)\).
CS proximity region is constructed with respect to the
interval \((a,b)\). This function works whether \(p_1\) and \(p_2\) are inside or outside the interval int.
Vertex regions for middle intervals are based on the center associated with the centrality parameter \(c \in (0,1)\). If \(p_1\) and \(p_2\) are identical, then it returns 1 regardless of their locations (i.e., loops are allowed in the digraph).
See also (ceyhan:revstat-2016;textualpcds).
IndNCSint(p1, p2, int, t, c = 0.5)\(I(p_2\) in \(N_{CS}(p_1,t,c))\) for p2, that is, returns 1 if \(p_2\) in \(N_{CS}(p_1,t,c)\), returns 0 otherwise
A 1D point for which the proximity region is constructed.
A 1D point for which it is checked whether it resides in the proximity region of \(p_1\) or not.
A vector of two real numbers representing an interval.
A positive real number which serves as the expansion parameter in CS proximity region.
A positive real number in \((0,1)\) parameterizing the center inside int\(=(a,b)\)
with the default c=.5.
For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\).
Elvan Ceyhan
IndNCSmid.int, IndNCSend.int and IndNPEint
c<-.4
t<-2
a<-0; b<-10; int<-c(a,b)
IndNCSint(7,5,int,t,c)
IndNCSint(1,3,int,t,c)
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