version 1.0.0

DESCRIPTION

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+Package: HOasso
+Type: Package
+Title: Higher Order Assortativity for Complex Networks
+Version: 1.0.0
+Date: 2023-07-21
+Authors@R: c(person("Alberto", "Arcagni", role = c("aut", "cre"), email = "alberto.arcagni@uniroma1.it"), person("Roy", "Cerqueti", role = c("aut")), person("Rosanna", "Grassi", role = c("aut")))
+Author: Alberto Arcagni [aut, cre],
+  Roy Cerqueti [aut],
+  Rosanna Grassi [aut]
+Description: Allows to evaluate Higher Order Assortativity of complex networks defined through objects of class 'igraph' from the package of the same name. The package returns a result also for directed and weighted graphs. References, Arcagni, A., Grassi, R., Stefani, S., & Torriero, A. (2017) <doi:10.1016/j.ejor.2017.04.028> Arcagni, A., Grassi, R., Stefani, S., & Torriero, A. (2021) <doi:10.1016/j.jbusres.2019.10.008> Arcagni, A., Cerqueti, R., & Grassi, R. (2023) <doi:10.48550/arXiv.2304.01737>.
+Depends: igraph, Rdpack
+RdMacros: Rdpack
+License: GPL (>= 2)
+Encoding: UTF-8
+NeedsCompilation: no
+Packaged: 2023-08-10 10:04:48 UTC; Alberto
+Maintainer: Alberto Arcagni <alberto.arcagni@uniroma1.it>
+Repository: CRAN
+Date/Publication: 2023-08-11 08:10:02 UTC

MD5

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+53cef403a3435cf508be10b7bf061a4f *DESCRIPTION
+740a27e00bcbc56143f5897b0f897cf2 *NAMESPACE
+cb5dde28544d0c2c5b72b3589eb9fb28 *R/HOasso.R
+d24568214203b863f387622b7c2db5f7 *build/partial.rdb
+88faf3510a569a1df58dd341d105b5c1 *inst/REFERENCES.bib
+9a60794edffbdbc41b2de921d45c8479 *man/HOasso.Rd

NAMESPACE

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+exportPattern("^[[:alpha:]]+")
+import("igraph")
+import("Rdpack")

R/HOasso.R

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+HOasso <- function(
+    g,
+    h = 1,
+    weighted = is.weighted(g),
+    x = c("sout", "dout", "lout", "sin", "din", "lin"),
+    y = c("sin", "din", "lin", "sout", "dout", "lout")
+) {
+
+  h <- round(max(h))
+
+  A <- W <- get.adjacency(g)
+  if (is.weighted(g))
+    W <- get.adjacency(g, attr = "weight")
+  din <- degree(g, mode = "in")
+  dout <- degree(g, mode = "out")
+  sin <- strength(g, mode = "in")
+  sout <- strength(g, mode = "out")
+  lin <- log(sin, 10)
+  lout <- log(sout, 10)
+
+  if (weighted) {
+    E <- W / sum(W)
+  } else {
+    E <- A / sum(A)
+  }
+
+  q0 <- rowSums(as.matrix(E))
+
+  Dinv <- 1 / q0
+  Dinv[is.infinite(Dinv)] <- 0
+  Dinv <- diag(Dinv)
+
+  P <- Dinv %*% E
+  Ph <- list(P)
+
+  if (h > 1)
+    for (i in 2:h)
+      Ph[[i]] <- Ph[[i - 1]] %*% P
+
+  Eh <- lapply(Ph, function(x) diag(q0) %*% x)
+
+  qh <- lapply(Eh, function(x) colSums(as.matrix(x)))
+
+  M <- list()
+  for (i in 1:h)
+    M[[i]] <- (Eh[[i]] - q0 %*% t(qh[[i]]))
+
+  x <- switch(x[1],
+              din = din,
+              dout = dout,
+              sin = sin,
+              sout = sout,
+              lin = lin,
+              lout = lout
+  )
+
+  y <- switch(y[1],
+              din = din,
+              dout = dout,
+              sin = sin,
+              sout = sout,
+              lin = lin,
+              lout = lout
+  )
+
+  num <- list()
+  for (i in 1:h)
+    num[[i]] <- t(x) %*% M[[i]] %*% y
+
+  Mx <- (diag(q0) - q0 %*% t(q0))
+
+  My <- list()
+  for (i in 1:h)
+    My[[i]] <- (diag(qh[[i]]) - qh[[i]] %*% t(qh[[i]]))
+
+  denX <- t(x) %*% Mx %*% x
+
+  denY <- list()
+  for (i in 1:h)
+    denY[[i]] <- t(y) %*% My[[i]] %*% y
+
+  res <- list()
+  for (i in 1:h)
+    res[[i]] <- as.numeric(num[[i]] / sqrt(denX * denY[[i]]))
+
+  res <- unlist(res)
+
+  sel <- abs(res) > 1
+  res[sel] <- NaN
+  if (any(sel, na.rm = TRUE)) {
+    warning(paste0("Error of approximation to zero of the covariance or a variance, ", sum(sel), "results forced to NaN"))
+  }
+
+  return(res)
+}

inst/REFERENCES.bib

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+@article{arcagni2017higher,
+  title={Higher order assortativity in complex networks},
+  author={Arcagni, Alberto and Grassi, Rosanna and Stefani, Silvana and Torriero, Anna},
+  journal={European Journal of Operational Research},
+  volume={262},
+  number={2},
+  pages={708--719},
+  year={2017},
+  publisher={Elsevier},
+  doi = {10.1016/j.ejor.2017.04.028}
+}
+
+@article{arcagni2021extending,
+  title={Extending assortativity: An application to weighted social networks},
+  author={Arcagni, Alberto and Grassi, Rosanna and Stefani, Silvana and Torriero, Anna},
+  journal={Journal of Business Research},
+  volume={129},
+  pages={774--783},
+  year={2021},
+  publisher={Elsevier},
+  doi = {10.1016/j.jbusres.2019.10.008}
+}
+
+@article{arcagni2023higher,
+  title={Higher order assortativity for directed weighted networks and Markov chains},
+  author={Arcagni, Alberto and Cerqueti, Roy and Grassi, Rosanna},
+  journal={arXiv preprint arXiv:2304.01737},
+  year={2023},
+  doi = {10.48550/arXiv.2304.01737}
+}

man/HOasso.Rd

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+\name{HOasso}
+\alias{HOasso}
+\title{Evalutes Higer Order Assortativity of complex networks}
+\usage{
+HOasso(
+    g,
+    h = 1,
+    weighted = is.weighted(g),
+    x = c("sout", "dout", "lout", "sin", "din", "lin"),
+    y = c("sin", "din", "lin", "sout", "dout", "lout")
+)
+}
+\arguments{
+\item{g}{an object of class \code{igraph} with two columns, listing the dominances, by rows.}
+\item{h}{an integer value, the function will evaluates the assortativity from the order 1 to the order \code{h}.}
+\item{weighted}{\code{logical}, if to use the weighted matrix to create the trasnition probabilities.}
+\item{x}{The first centrarlity measure, out-strength by default, see \code{details}.}
+\item{y}{The second centrarlity measure, in-strength by default, see \code{details}.}
+}
+\value{A vector \code{h} long containing the assortativity measures from the order 1 to the order \code{h}.}
+\description{
+The function evalutes Higer Order Assortativity of complex networks represented by objects of class \code{igraph} from the package of the same name.
+}
+\details{
+Arguments \code{x} and {y} are \code{character} objects and can assume values   \code{"sout"}, \code{"dout"}, \code{"lout"}, \code{"sin"}, \code{"din"}, \code{"lin"} representing the out-strength, out-degree, out-log-strength, in-strength, in-degree, and in-log-strength respectively.
+
+In case of undirected graphs in- and out- centrality measures are equal. In case of unweighted graphs the strength is equal to the degree.
+}
+\references{
+\insertRef{arcagni2017higher}{HOasso}
+
+\insertRef{arcagni2021extending}{HOasso}
+
+\insertRef{arcagni2023higher}{HOasso}
+}
+\examples{
+  g <- graph_from_data_frame(data.frame(
+    from   = c("i", "j", "j", "k", "l"),
+    to     = c("k", "k", "l", "l", "i"),
+    weight = c( 10,  5,   2,   3,   2 )
+  ))
+  E(g)$label <- E(g)$weight
+  plot(g, layout = layout_in_circle(g))
+  a <- HOasso(g, h = 10)
+  a
+  plot(a, type = "b", ylim = c(-1, 1), panel.first = abline(h = 0, lty = 2))
+}