powernet -- algebraic graphs with edges labeled by capacity

This package implements Networks, graph data structures where edges are labeled by capacity.

A Network is typically constructed algebraically using -<, >-, and overlays:

import Data.Network

node1 = node 'a' 1
node2 = node 'b' 2
node3 = node 'c' 3

type NodeLabel = Char
type NodeContent = Int

network :: Network Int NodeLabel NodeContent
network = overlays [ node1 -< (10 :: Capacity Int) >- node2
                   , node2 -< (15 :: Capacity Int) >- node3
                   , node3 -< ( 7 :: Capacity Int) >- node1
                   ]

See the documentation for Data.Network (run cabal haddock) for documentation on the various operations available.

Implementation details

This library builds on algebraic graphs provided by algebraic-graphs.

Why another library? Not all instances of algebraic-graphs make sense at the time of writing these words. Consider this code:

import Algebra.Graph.Labelled 

graph :: Graph (Capacity Int) Char
graph = edges [(0, 'a', 'b'), (0, 'b', 'c'), (0, 'c', 'a')]

What would you expect for length graph and traverse print graph? The internal structure of Algebra.Graph.Labelled.Graph leaks such that the Foldable and Traversable instances may behave unintuitively.

powernet solves this problem by separating the topology of the network, and the nodes (and their contents). Roughly:

type NodeID = Int

data Network e a 
    = MkNetwork { networkTopology :: Graph (Capacity e) NodeID
                , networkNodeMap  :: Bimap NodeID a
                }

In this implementation, Network has intuitive Foldable and Traversable instances.