R/paths.R

In igraph: Network Analysis and Visualization

## -----------------------------------------------------------------------
##
##   IGraph R package
##   Copyright (C) 2014  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.
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##   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.
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##   along with this program; if not, write to the Free Software
##   Foundation, Inc.,  51 Franklin Street, Fifth Floor, Boston, MA
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## -----------------------------------------------------------------------

#' List all simple paths from one source
#'
#' This function lists are simple paths from one source vertex to another
#' vertex or vertices. A path is simple if the vertices it visits are not
#' visited more than once.
#'
#' Note that potentially there are exponentially many paths between two
#' vertices of a graph, and you may run out of memory when using this
#' function, if your graph is lattice-like.
#'
#' This function currently ignored multiple and loop edges.
#'
#' @param graph The input graph.
#' @param from The source vertex.
#' @param to The target vertex of vertices. Defaults to all vertices.
#' @param mode Character constant, gives whether the shortest paths to or
#'   from the given vertices should be calculated for directed graphs. If
#'   `out` then the shortest paths *from* the vertex, if `in`
#'   then *to* it will be considered. If `all`, the default, then
#'   the corresponding undirected graph will be used, i.e. not directed paths
#'   are searched. This argument is ignored for undirected graphs.
#' @param cutoff Maximum length of path that is considered. If negative, paths of all lengths are considered.
#' @return A list of integer vectors, each integer vector is a path from
#'   the source vertex to one of the target vertices. A path is given by its
#'   vertex ids.
#' @keywords graphs
#' @examples
#'
#' g <- make_ring(10)
#' all_simple_paths(g, 1, 5)
#' all_simple_paths(g, 1, c(3, 5))
#'
#' @family paths
#' @export
all_simple_paths <- function(graph, from, to = V(graph),
                             mode = c("out", "in", "all", "total"),
                             cutoff = -1) {
  ## Argument checks
  ensure_igraph(graph)
  from <- as_igraph_vs(graph, from)
  to <- as_igraph_vs(graph, to)
  mode <- switch(igraph.match.arg(mode),
    "out" = 1,
    "in" = 2,
    "all" = 3,
    "total" = 3
  )

  on.exit(.Call(R_igraph_finalizer))

  ## Function call
  res <- .Call(
    R_igraph_get_all_simple_paths, graph, from - 1, to - 1,
    as.integer(cutoff), mode
  )
  res <- get.all.simple.paths.pp(res)

  if (igraph_opt("return.vs.es")) {
    res <- lapply(res, unsafe_create_vs, graph = graph, verts = V(graph))
  }
  res
}


#' Directed acyclic graphs
#'
#' This function tests whether the given graph is a DAG, a directed acyclic
#' graph.
#'
#' `is_dag()` checks whether there is a directed cycle in the graph. If not,
#' the graph is a DAG.
#'
#' @aliases is.dag is_dag
#' @param graph The input graph. It may be undirected, in which case
#'   `FALSE` is reported.
#' @return A logical vector of length one.
#' @author Tamas Nepusz \email{ntamas@@gmail.com} for the C code, Gabor Csardi
#' \email{csardi.gabor@@gmail.com} for the R interface.
#' @keywords graphs
#' @examples
#'
#' g <- make_tree(10)
#' is_dag(g)
#' g2 <- g + edge(5, 1)
#' is_dag(g2)
#' @family cycles
#' @family structural.properties
#' @export
is_dag <- is_dag_impl


#' Maximum cardinality search
#'
#' Maximum cardinality search is a simple ordering a vertices that is useful in
#' determining the chordality of a graph.
#'
#' Maximum cardinality search visits the vertices in such an order that every
#' time the vertex with the most already visited neighbors is visited. Ties are
#' broken randomly.
#'
#' The algorithm provides a simple basis for deciding whether a graph is
#' chordal, see References below, and also [is_chordal()].
#'
#' @aliases maximum.cardinality.search max_cardinality
#' @param graph The input graph. It may be directed, but edge directions are
#'   ignored, as the algorithm is defined for undirected graphs.
#' @return A list with two components: \item{alpha}{Numeric vector. The
#'   1-based rank of each vertex in the graph such that the vertex with rank 1
#'   is visited first, the vertex with rank 2 is visited second and so on.}
#'   \item{alpham1}{Numeric vector. The inverse of `alpha`. In other words,
#'   the elements of this vector are the vertices in reverse maximum cardinality
#'   search order.}
#' @author Gabor Csardi \email{csardi.gabor@@gmail.com}
#' @seealso [is_chordal()]
#' @references Robert E Tarjan and Mihalis Yannakakis. (1984). Simple
#' linear-time algorithms to test chordality of graphs, test acyclicity of
#' hypergraphs, and selectively reduce acyclic hypergraphs.  *SIAM Journal
#' of Computation* 13, 566--579.
#' @keywords graphs
#' @export
#' @examples
#'
#' ## The examples from the Tarjan-Yannakakis paper
#' g1 <- graph_from_literal(
#'   A - B:C:I, B - A:C:D, C - A:B:E:H, D - B:E:F,
#'   E - C:D:F:H, F - D:E:G, G - F:H, H - C:E:G:I,
#'   I - A:H
#' )
#' max_cardinality(g1)
#' is_chordal(g1, fillin = TRUE)
#'
#' g2 <- graph_from_literal(
#'   A - B:E, B - A:E:F:D, C - E:D:G, D - B:F:E:C:G,
#'   E - A:B:C:D:F, F - B:D:E, G - C:D:H:I, H - G:I:J,
#'   I - G:H:J, J - H:I
#' )
#' max_cardinality(g2)
#' is_chordal(g2, fillin = TRUE)
#' @family chordal
max_cardinality <- maximum_cardinality_search_impl


#' Eccentricity of the vertices in a graph
#'
#' The eccentricity of a vertex is its shortest path distance from the farthest
#' other node in the graph.
#'
#' The eccentricity of a vertex is calculated by measuring the shortest
#' distance from (or to) the vertex, to (or from) all vertices in the graph,
#' and taking the maximum.
#'
#' This implementation ignores vertex pairs that are in different components.
#' Isolate vertices have eccentricity zero.
#'
#' @param graph The input graph, it can be directed or undirected.
#' @param vids The vertices for which the eccentricity is calculated.
#' @param mode Character constant, gives whether the shortest paths to or from
#'   the given vertices should be calculated for directed graphs. If `out`
#'   then the shortest paths *from* the vertex, if `in` then *to*
#'   it will be considered. If `all`, the default, then the corresponding
#'   undirected graph will be used, edge directions will be ignored. This
#'   argument is ignored for undirected graphs.
#' @return `eccentricity()` returns a numeric vector, containing the
#'   eccentricity score of each given vertex.
#' @seealso [radius()] for a related concept,
#'   [distances()] for general shortest path calculations.
#' @references Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35,
#' 1994.
#' @examples
#' g <- make_star(10, mode = "undirected")
#' eccentricity(g)
#' @family paths
#' @export
eccentricity <- eccentricity_impl


#' Radius of a graph
#'
#' The eccentricity of a vertex is its shortest path distance from the
#' farthest other node in the graph. The smallest eccentricity in a graph
#' is called its radius
#'
#' The eccentricity of a vertex is calculated by measuring the shortest
#' distance from (or to) the vertex, to (or from) all vertices in the
#' graph, and taking the maximum.
#'
#' This implementation ignores vertex pairs that are in different
#' components.  Isolate vertices have eccentricity zero.
#'
#' @param graph The input graph, it can be directed or undirected.
#' @param mode Character constant, gives whether the shortest paths to or from
#'   the given vertices should be calculated for directed graphs. If `out`
#'   then the shortest paths *from* the vertex, if `in` then *to*
#'   it will be considered. If `all`, the default, then the corresponding
#'   undirected graph will be used, edge directions will be ignored. This
#'   argument is ignored for undirected graphs.
#' @return A numeric scalar, the radius of the graph.
#' @seealso [eccentricity()] for the underlying
#'   calculations, code{[distances]} for general shortest path
#'   calculations.
#' @references Harary, F. Graph Theory. Reading, MA: Addison-Wesley, p. 35,
#' 1994.
#' @examples
#' g <- make_star(10, mode = "undirected")
#' eccentricity(g)
#' radius(g)
#' @family paths
#' @export
radius <- radius_impl

#' @rdname distances
#' @param directed Whether to consider directed paths in directed graphs,
#'   this argument is ignored for undirected graphs.
#' @family paths
#' @export
distance_table <- path_length_hist_impl