# SimpleWeightedGraphs

Edge-Weighted Graphs for LightGraphs.jl.

Usage:

```
using LightGraphs, SimpleWeightedGraphs
g = SimpleWeightedGraph(3) # or use `SimpleWeightedDiGraph` for directed graphs
add_edge!(g, 1, 2, 0.5)
add_edge!(g, 2, 3, 0.8)
add_edge!(g, 1, 3, 2.0)
# find the shortest path from vertex 1 to vertex 3 taking weights into account.
enumerate_paths(dijkstra_shortest_paths(g, 1), 3)
3-element Array{Int64,1}:
1
2
3
# reweight the edge from 1 to 2
add_edge!(g, 1, 2, 1.6)
# rerun the shortest path calculation from 1 to 3
enumerate_paths(dijkstra_shortest_paths(g, 1), 3)
2-element Array{Int64,1}:
1
3
# it's possible to build the graph from arrays of sources, destinations and weights
sources = [1,2,1]
destinations = [2,3,3]
weights = [0.5, 0.8, 2.0]
g = SimpleWeightedGraph(sources, destinations, weights)
# the combine keyword handles repeated pairs (sum by default)
g = SimpleWeightedGraph([1,2,1], [2,1,2], [1,1,1]; combine = +)
g.weights[2,1] == g.weights[1,2] == 3 # true
# WARNING: unexpected results might occur with non-associative combine functions
# notice that weights are indexed by [destination, source]
s = SimpleWeightedDiGraph([1,2,1], [2,1,2], [1,1,1]; combine = +)
s.weights[1,2] == 1 # true
s.weights[2,1] == 2 # true
```

Please pay attention to the fact that zero-weight edges are discarded by `add_edge!`

.
This is due to the way the graph is stored (a sparse matrix). A possible workaround
is to set a very small weight instead.

Note that adding or removing vertices or edges from these graph types is not particularly performant; see MetaGraphs.jl for possible alternatives.