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\begin{document}
\title{Experimental Support for Multigraphs}
\author{Seth Falcon}
\maketitle

\SweaveOpts{keep.source=TRUE}

<<funcs, echo=FALSE, results=hide>>=
st <- system.time

@

\section{Introduction}

  The MultiGraph class represents a single node set and a set of edge
  sets.  Each edge set is either directed or undirected.  We can think
  of an edge in a MultiGraph as a 4-tuple (from-node, to-node,
  edge-type, weight), where the edge-type field in the tuple identifies
  the edge set, the weight is a numeric value, and the order of the
  nodes only matters in the case of a directed edge set.  Unlike some of
  the graph representations, self-loops are allowed (from-node ==
  to-node).

  There is support for arbitrary edge attributes which is primarily
  useful for rendering plots of MultiGraphs.  These attributes are
  stored separately from the edge weights to facilitate efficient edge
  weight computation.

<<setup>>=
library("graph")
set.seed(0xab34eL)
ft1 <- graph:::randFromTo(10000L, 1e6L)
ft2 <- graph:::randFromTo(10000L, 1e6L)
ft3 <- graph:::randFromTo(30000L, 1e6L)

names(ft1)
head(ft1$nodes)
head(ft1$ft)

esets <- list(e1=ft1$ft, e2=ft2$ft, e3=ft3$ft)
## order(to_i, from_i) is a big factor here
st(g <- MultiGraph(esets))

object.size(esets) / 1024^2
object.size(g) / 1024^2
g
numNodes(g)
## we should be able to make numEdges faster by
## memoizing and/or just taking length of weight
## vector.
st(numEdges(g))
st(lapply(eweights(g), head))
## this is slow because of string creation, I suspect
st(lapply(eweights(g, "=>"), head))

## a good portion is in new and initialize
st(gi <- edgeSetIntersect0(g))
gi

st(degree(g))
st(extractFromTo(g))

nds <- nodes(g)
subNds <- sample(nds,0.5*length(nds))
st(subGraph(subNds,g))

@

\end{document}