R/degseq.R

In igraph: Network Analysis and Visualization

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##   IGraph R package
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#' Check if a degree sequence is valid for a multi-graph
#'
#' `is_degseq()` checks whether the given vertex degrees (in- and
#' out-degrees for directed graphs) can be realized by a graph. Note that the
#' graph does not have to be simple, it may contain loop and multiple edges.
#' For undirected graphs, it also checks whether the sum of degrees is even.
#' For directed graphs, the function checks whether the lengths of the two
#' degree vectors are equal and whether their sums are also equal. These are
#' known sufficient and necessary conditions for a degree sequence to be valid.
#'
#' @aliases is.degree.sequence is_degseq
#' @param out.deg Integer vector, the degree sequence for undirected graphs, or
#'   the out-degree sequence for directed graphs.
#' @param in.deg `NULL` or an integer vector. For undirected graphs, it
#'   should be `NULL`. For directed graphs it specifies the in-degrees.
#' @return A logical scalar.
#' @author Tamas Nepusz \email{ntamas@@gmail.com} and Szabolcs Horvat \email{szhorvat@gmail.com}
#' @references Z Kiraly, Recognizing graphic degree sequences and generating
#' all realizations. TR-2011-11, Egervary Research Group, H-1117, Budapest,
#' Hungary. ISSN 1587-4451 (2012).
#'
#' B. Cloteaux, Is This for Real? Fast Graphicality Testing, *Comput. Sci. Eng.* 17, 91 (2015).
#'
#' A. Berger, A note on the characterization of digraphic sequences, *Discrete Math.* 314, 38 (2014).
#'
#' G. Cairns and S. Mendan, Degree Sequence for Graphs with Loops (2013).
#'
#' @keywords graphs
#'
#' @family graphical degree sequences
#' @examples
#' g <- sample_gnp(100, 2 / 100)
#' is_degseq(degree(g))
#' is_graphical(degree(g))
#' @export
is_degseq <- function(out.deg, in.deg = NULL) {
  is_graphical(out.deg, in.deg, allowed.edge.types = "all")
}

#' Is a degree sequence graphical?
#'
#' Determine whether the given vertex degrees (in- and out-degrees for
#' directed graphs) can be realized by a graph.
#'
#' The classical concept of graphicality assumes simple graphs. This function
#' can perform the check also when self-loops, multi-edges, or both are allowed
#' in the graph.
#'
#' @aliases is.graphical.degree.sequence
#' @param out.deg Integer vector, the degree sequence for undirected graphs, or
#'   the out-degree sequence for directed graphs.
#' @param in.deg `NULL` or an integer vector. For undirected graphs, it
#'   should be `NULL`. For directed graphs it specifies the in-degrees.
#' @param allowed.edge.types The allowed edge types in the graph. \sQuote{simple}
#'   means that neither loop nor multiple edges are allowed (i.e. the graph must be
#'   simple). \sQuote{loops} means that loop edges are allowed but mutiple edges
#'   are not. \sQuote{multi} means that multiple edges are allowed but loop edges
#'   are not. \sQuote{all} means that both loop edges and multiple edges are
#'   allowed.
#' @return A logical scalar.
#' @author Tamas Nepusz \email{ntamas@@gmail.com}
#' @references Hakimi SL: On the realizability of a set of integers as degrees
#' of the vertices of a simple graph. *J SIAM Appl Math* 10:496-506, 1962.
#'
#' PL Erdos, I Miklos and Z Toroczkai: A simple Havel-Hakimi type algorithm to
#' realize graphical degree sequences of directed graphs.  *The Electronic
#' Journal of Combinatorics* 17(1):R66, 2010.
#' @keywords graphs
#'
#' @family graphical degree sequences
#' @examples
#' g <- sample_gnp(100, 2 / 100)
#' is_degseq(degree(g))
#' is_graphical(degree(g))
#' @export
is_graphical <- is_graphical_impl