```
#' Generates an incidence matrix with a given cell-filling probability
#'
#' `incidence.from.probability` generates a random incidence matrix in which each cell is filled
#' with a 1 with a given probability.
#'
#' @param R integer: number of rows
#' @param C integer: number of columns
#' @param P numeric: probability that a cell contains a 1; if P = 0 a probability will be chosen randomly
#' @param constrain boolean: ensure that no rows or columns sum to 0 (i.e., contain all 0s) or to 1 (i.e., contain all 1s)
#' @param class string: the class of the returned backbone graph, one of c("matrix", "Matrix", "igraph").
#' @param narrative boolean: TRUE if suggested text & citations should be displayed.
#'
#' @return
#' An incidence matrix of class `matrix` or `Matrix`, or a bipartite graph of class {\link{igraph}}.
#'
#' @references {Neal, Z. P., Domagalski, R., and Sagan, B. 2021. Comparing alternatives to the fixed degree sequence model for extracting the backbone of bipartite projections. *Scientific Reports, 11*, 23929. \doi{10.1038/s41598-021-03238-3}}
#' @references {Neal, Z. P. 2022. incidentally: An R package to generate incidence matrices and bipartite graphs. *OSF Preprints* \doi{10.31219/osf.io/ectms}}
#'
#' @export
#'
#' @examples
#' I <- incidence.from.probability(R = 10, C = 10)
#' I <- incidence.from.probability(R = 10, C = 10, P = .5)
#' I <- incidence.from.probability(R = 10, C = 10, P = .5,
#' class = "igraph", narrative = TRUE)
incidence.from.probability <- function(R, C, P=0, constrain = TRUE, class="matrix", narrative = FALSE) {
#Parameter check
if (!is.numeric(R) | !is.numeric(C) | !is.numeric(P)) {stop("R, C, and P must be numeric")}
if (R<0 | C<0 | R%%1!=0 | C%%1!=0) {stop("R and C must be positive integers")}
if (P<0 | P>1) {stop("P must be between 0 and 1")}
#Check or pick probability
if (constrain) {
minP <- max(R,C) / (R*C) #Minimum probability if marginal constraints are imposed
maxP <- ((R*C) - max(R,C)) / (R*C) #Maximum probability
if (P == 0) {P <- stats::runif(1, min = minP, max = maxP)} #If unspecified, pick a probability
if (P < minP | P > maxP) {stop("P is outside the allowed range for this size bipartite network")}
} else {if (P == 0) {P <- stats::runif(1)}}
#Create an incidence matrix
I <- matrix(stats::rbinom(R*C,1,P),R,C)
#Repeat until constraints are satisfied
if (constrain) {
while (min(rowSums(I))==0 | max(rowSums(I))==C | min(colSums(I))==0 | max(colSums(I))==R ) {I <- matrix(stats::rbinom(R*C,1,P),R,C)}
}
#Convert to desired class and return
if (class == "igraph"){I <- igraph::graph_from_incidence_matrix(I)}
if (class == "Matrix"){I <- Matrix::Matrix(I)}
#Display narrative if requested
if (narrative) {
version <- utils::packageVersion("incidentally")
if (class == "igraph") {text <- paste0("We used the incidentally package for R (v", version, "; Neal, 2022) to generate a random bipartite graph with ", R, " agents and ", C, " artifacts, where there was a ", round(P,2), " probability that a given agent was connected to a given artifact.")}
if (class != "igraph") {text <- paste0("We used the incidentally package for R (v", version, "; Neal, 2022) to generate a random incidence matrix with ", R, " rows and ", C, " columns, where there was a ", round(P,2), " probability that the ith row and kth column contained a 1.")}
message("")
message("=== Suggested manuscript text and citations ===")
message(text)
message("")
message("Neal, Z. P. (2022). incidentally: An R package to generate incidence matrices and bipartite graphs. OSF Preprints. https://doi.org/10.31219/osf.io/ectms")
}
return(I)
}
```

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