Introduce a PartitionedGraph Type

[JoeyT1994]

We should introduce a PartitionedGraph structure. Ideally this should be separate from NamedGraphs and just be an abstract graph type with the relevant functionality. For now though we will make a PartitionedGraphs.jl submodule within NamedGraphs.jl.

The general structure could look like

abstract type AbstractPartitionedGraph{V,PV} <: AbstractGraph{V} end

struct PartitionedGraph{V,PV,G<:AbstractGraph{V},PG<:AbstractGraph{PV}} <: AbstractPartitionedGraph{PV}
  graph::G
  partioned_graph::PG
  partition_vertices::Dictionary{PV,Vector{V}}
  partition::Dictionary{V,PV}
end

such that a partitioned graph essentially consists of two graphs: the original graph G and the partitioned graph PG. The structure then also contains a map (and its reverse) between the subsets of vertices of G which consistute the vertices of PG.

We then need to define functionality for this structure. It would make sense to define standard Graphs.jl calls on a PartitionedGraph to pass to the original graph G. For instance vertices(pg::PartitionedGraph) = vertices(pg.G) Then we define partitioned versions of those calls which operate on PG instead. E.g. partitioned_vertices(pg::PartitionedGraph) = vertices(pg.PG).
Other examples of such functions might be has_vertex versus partitioned_has_vertex, is_tree versus partitioned_is_tree etc.

Helpful functions might then be determining whether an edge of G is within a partition or between partitions. And which partitions.
E.g

function edge_partitions(e::AbstractEdge, PG::PartitionedGraph)
   return find_key(PG.partition, src(e)), find_key(PG.partition, dst(e))
end

function edge_in_partition(e::AbstractEdge, PG::PartitionedGraph)
  return all_equal(edge_partitions(e, PG))
end

Another question is whether we define types such as PartitionedVertex and PartitionedEdge so that calls such as has_vertex(PG, PartitionedVertex(1)) pass directly to partitioned_has_vertex. This is mostly for convenience.

@mtfishman

[JoeyT1994]

We should also define default constructors for a PartitionedGraph.

For instance PartitionedGraph(G::AbstractGraph, partition_vertices::Vector{Vector{V}}) should return a partitioned graph which defaults to integer naming for the vertices of PG. This works by constructing the relevant dictionary with integer keys and passing to the constructor PartitionedGraph(G::AbstractGraph, partition_vertices::Dictionary{PV,Vector{V}}).

Meanwhile we should consider constructors such as PartitionedGraph(G::AbstractGraph, npartitions::Integer; kwargs) which constructs a partitioned graph from G (defaulting to integer naming) with npartitions. The default construction could be via some sort min_cut search and corresponding algorithms already exist in KaHyPar and Metis. This would supersede the current functionality in ITensorNetworks/src/partition.jl which has some code for partitioned_graphs.

[mtfishman]

Closed by #44.