# The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - one interval case An object of class `"PCDs"`. Returns arcs of CS-PCD as tails (or sources) and heads (or arrow ends) and related parameters and the quantities of the digraph. The vertices of the CS-PCD are the 1D data points in `Xp` in the one interval case. `int` determines the end points of the interval. For this function, CS proximity regions are constructed data points inside or outside the interval based on `int` points with expansion parameter $t > 0$ and centrality parameter $c \in (0,1)$. That is, for this function, arcs may exist for points in the middle or end-intervals. It also provides various descriptions and quantities about the arcs of the CS-PCD such as number of arcs, arc density, etc. ```r arcsCSint(Xp, int, t, c = 0.5) ``` ## Arguments - `Xp`: A set or `vector` of 1D points which constitute the vertices of the CS-PCD. - `int`: A `vector` of two 1D points which constitutes the end points of the interval. - `t`: A positive real number which serves as the expansion parameter in CS proximity region. - `c`: A positive real number in $(0,1)$ parameterizing the center inside middle intervals with the default `c=.5`. For the interval, `int`$=(a,b)$, the parameterized center is $M_c=a+c(b-a)$. ## Returns A `list` with the elements - **type**: A description of the type of the digraph - **parameters**: Parameters of the digraph, here, they are expansion and centrality parameters. - **tess.points**: Tessellation points, i.e., points on which the tessellation of the study region is performed, here, tessellation is the intervalization of the real line based on `int` points. - **tess.name**: Name of the tessellation points `tess.points` - **vertices**: Vertices of the digraph, `Xp` points - **vert.name**: Name of the data set which constitute the vertices of the digraph - **S**: Tails (or sources) of the arcs of CS-PCD for 1D data - **E**: Heads (or arrow ends) of the arcs of CS-PCD for 1D data - **mtitle**: Text for `"main"` title in the plot of the digraph - **quant**: Various quantities for the digraph: number of vertices, number of partition points, number of intervals, number of arcs, and arc density. ## Examples ```r tau<-2 c<-.4 a<-0; b<-10; int<-c(a,b); #n is number of X points n<-10; #try also n<-20 xf<-(int[2]-int[1])*.1 set.seed(1) Xp<-runif(n,a-xf,b+xf) Arcs<-arcsCSint(Xp,int,tau,c) Arcs summary(Arcs) plot(Arcs) Xp<-runif(n,a+10,b+10) Arcs=arcsCSint(Xp,int,tau,c) Arcs summary(Arcs) plot(Arcs) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `arcsCS1D`, `arcsCSmid.int`, `arcsCSend.int`, and `arcsPE1D` ## Author(s) Elvan Ceyhan

arcsCSint function