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## -----------------------------------------------------------------------
##
## IGraph R package
## Copyright (C) 2015 Gabor Csardi <csardi.gabor@gmail.com>
## 334 Harvard street, Cambridge, MA 02139 USA
##
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, write to the Free Software
## Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
## 02110-1301 USA
##
## -----------------------------------------------------------------------
#' Check if a degree sequence is valid for a multi-graph
#'
#' \code{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 \code{NULL} or an integer vector. For undireted graphs, it
#' should be \code{NULL}. For directed graphs it specifies the in-degrees.
#' @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. \emph{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. \emph{The Electronic
#' Journal of Combinatorics} 17(1):R66, 2010.
#' @keywords graphs
#'
#' @family graphical degree sequences
#'
#' g <- sample_gnp(100, 2/100)
#' is_degseq(degree(g))
#' is_graphical(degree(g))
#' @export
#' @include auto.R
is_degseq <- is_degseq
#' Is a degree sequence graphical?
#'
#' Determine whether the given vertex degrees (in- and out-degrees for
#' directed graphs) can be reliazed in a simple graph, i.e. a graph without
#' multiple or loop edges.
#'
#' @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 \code{NULL} or an integer vector. For undireted graphs, it
#' should be \code{NULL}. For directed graphs it specifies the in-degrees.
#' @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. \emph{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. \emph{The Electronic
#' Journal of Combinatorics} 17(1):R66, 2010.
#' @keywords graphs
#'
#' @family graphical degree sequences
#'
#' g <- sample_gnp(100, 2/100)
#' is_degseq(degree(g))
#' is_graphical(degree(g))
#' @export
#' @include auto.R
is_graphical <- is_graphical
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