# Graphs.jl interface

```
using Graphs
using MetaGraphsNext
```

`MetaGraph`

s inherit many methods from Graphs.jl. In general, inherited methods refer to vertices by codes, not labels, for compatibility with the `AbstractGraph`

interface.

Note that vertex codes get reassigned after `rem_vertex!`

operations to remain contiguous, so we recommend systematically converting to and from labels.

## Undirected graphs

We can make `MetaGraph`

s based on (undirected) `Graph`

s.

```
cities = MetaGraph(
Graph();
label_type=Symbol,
vertex_data_type=String,
edge_data_type=Int,
graph_data=nothing,
weight_function=identity,
);
```

Let us add some cities and the distance between them:

```
cities[:Paris] = "France";
cities[:London] = "UK";
cities[:Berlin] = "Germany";
cities[:Paris, :London] = 344;
cities[:Paris, :Berlin] = 878;
```

The general properties of the graph are as expected:

`is_directed(cities)`

`false`

`eltype(cities)`

`Int64`

`edgetype(cities)`

`Graphs.SimpleGraphs.SimpleEdge{Int64}`

We can check the set of vertices:

`nv(cities)`

`3`

`collect(vertices(cities))`

```
3-element Vector{Int64}:
1
2
3
```

`has_vertex(cities, 2)`

`true`

`has_vertex(cities, 4)`

`false`

Note that we can't add the same city (i.e. vertex label) twice:

`add_vertex!(cities, :London, "Italy")`

`false`

`nv(cities)`

`3`

`cities[:London]`

`"UK"`

We then check the set of edges:

`ne(cities)`

`2`

`collect(edges(cities))`

```
2-element Vector{Graphs.SimpleGraphs.SimpleEdge{Int64}}:
Edge 1 => 2
Edge 1 => 3
```

`has_edge(cities, 1, 2)`

`true`

`has_edge(cities, 2, 3)`

`false`

From this initial graph, we can create some others:

`copy(cities)`

`Meta graph based on a SimpleGraph{Int64} with vertex labels of type Symbol, vertex metadata of type String, edge metadata of type Int64, graph metadata given by nothing, and default weight 1.0`

`zero(cities)`

`Meta graph based on a SimpleGraph{Int64} with vertex labels of type Symbol, vertex metadata of type String, edge metadata of type Int64, graph metadata given by nothing, and default weight 1.0`

Since `cities`

is a weighted graph, we can leverage the whole Graphs.jl machinery of graph analysis and traversal:

`diameter(cities)`

`1222.0`

`ds = dijkstra_shortest_paths(cities, 2)`

`Graphs.DijkstraState{Float64, Int64}([2, 0, 1], [344.0, 0.0, 1222.0], [Int64[], Int64[], Int64[]], [1.0, 1.0, 1.0], Int64[])`

Finally, let us remove some edges and vertices

```
rem_edge!(cities, 1, 3);
rem_vertex!(cities, 3);
has_vertex(cities, 1) && !has_vertex(cities, 3)
```

`true`

## Directed graphs

We can make `MetaGraph`

s based on `DiGraph`

s as well.

```
rock_paper_scissors = MetaGraph(DiGraph(); label_type=Symbol, edge_data_type=String);
for label in [:rock, :paper, :scissors]
rock_paper_scissors[label] = nothing
end
rock_paper_scissors[:rock, :scissors] = "rock beats scissors"
rock_paper_scissors[:scissors, :paper] = "scissors beat paper"
rock_paper_scissors[:paper, :rock] = "paper beats rock";
```

We see that the underlying graph has changed:

`is_directed(rock_paper_scissors)`

`true`

Directed graphs can be reversed:

`haskey(rock_paper_scissors, :scissors, :rock)`

`false`

`haskey(reverse(rock_paper_scissors), :scissors, :rock)`

`true`

Let us take a subgraph induced by a subset of vertices:

`rock_paper, _ = induced_subgraph(rock_paper_scissors, [1, 2])`

`(Meta graph based on a SimpleDiGraph{Int64} with vertex labels of type Symbol, vertex metadata of type Nothing, edge metadata of type String, graph metadata given by nothing, and default weight 1.0, [1, 2])`

`issubset(rock_paper, rock_paper_scissors)`

`true`

`haskey(rock_paper, :paper, :rock)`

`true`

`haskey(rock_paper, :rock, :scissors)`

`false`

Subgraphs can also be induced by a subset of edges.

```
subtree_edges = collect(edges(rock_paper_scissors))[2:3]
rock_paper_scissors_subtree, _ = induced_subgraph(rock_paper_scissors, subtree_edges)
issubset(rock_paper_scissors_subtree, rock_paper_scissors)
ne(rock_paper_scissors_subtree)
```

`2`

`nv(rock_paper_scissors_subtree)`

`3`

`[rock_paper_scissors_subtree[e...] for e in edge_labels(rock_paper_scissors_subtree)]`

```
2-element Vector{String}:
"paper beats rock"
"scissors beat paper"
```

Checking that a graph is a subset of another is not supported yet. For example, an induced subgraph may appear as not a subset of the original graph, if vertex codes were modified.

`issubset(rock_paper_scissors_subtree, rock_paper_scissors)`

`false`

```
rock_scissors, _ = induced_subgraph(rock_paper_scissors, [1, 3])
issubset(rock_scissors, rock_paper_scissors)
```

`false`

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