# Digraph library Digraph is a very simple, C++ 11 template-based, directed graph library. It is not designed to be general, but to suit the needs of the (next) Faust compiler.

It is made of two files:

• `digraph.hh` the digraph class
• `digraphop.hh` some operations on digraphs

## Building a digraph

A digraph is a directed graph. It is composed of a set of nodes `{n_1,n_2,...}` and a set of connections (i.e. arrows) between these nodes `{(n_i -d-> n_j),...}`.

For a connection `(n_i -d-> n_j)`, the node `n_i` is the source of the connection, the node `n_j` is the destination of the connections, and the integer `d` is the value of the connection. When the value is not specified its is by default 0.

The API to create a graph is very simple. You start by creating an empty graph:

``digraph<char> g;``

Then you add nodes and connections to the graph:

``g.add('A','B').add('B','C',1).add('D')...``

The method `add()` can be used to add individual nodes like in `add('D')` or connections `add('A','B')`. In this case, the involved nodes are automatically added to the graph. There is no need to add them individually.

By default the value of the connection is 0. To create a connection with a different value use: `add('A','B',3)`. If multiple connections between two nodes are created, only the connection with the smallest value is kept.

It is also possible to `add()` a whole graph with all its nodes and connections. For example if `g1` and `g2` are two graphs, then:

``g1.add(g2)``

Will add all the nodes and connections of `g2` into `g1`. If multiple connections between two nodes are created, only the connection with the smallest value is kept.

Please note that the only way to modify a digraphs is by adding nodes and connections using the `add()` method. Digraphs are otherwise immutable, and all other transformation implies the creation of a new digraph.

## Accessing nodes and connections

To access the nodes of a graph, one uses the method `g.nodes()`. For example to iterate over the nodes:

``````for (const auto& n : g.nodes()) {
... do something with node n ...
}``````

Once you have a node you can iterate over its connections. To access the connections of a node we use the method `g.connections(n)`:

``````for (const auto& n : g.nodes()) {
for (const auto& c : g.connections(n)) {
... c.first: destination node of the connection
... c.second: value of the connection
}
}``````

## Algorithms and Operations on digraphs

Please note that the following operations never modify the graphs used as arguments.

### Partition

A partition of a digraph into strongly connected components can be obtained using the Tarjan class, an implementation of Robert Tarjan's algorithm

``````Tarjan<N> t(const digraph<N>&);
...t.partition()...``````

The Tarjan class has essentially two methods:

#### Partition

The method `partition()` returns the partition of the graph into strongly connected components.

``partition() -> set<set<N>>&``

The result is a set of set on nodes. Each set of nodes represents a strongly connected component of the graph.

#### Cycles

The method `cycles()` returns the number of cycles of the graph.

``cycles() -> int``

### Number of cycles

The function `cycles(mygraph)` return the number of cycles of a graph. It uses internally `Tarjan`.

``cycles(const digraph<N>&) -> int``

### Direct acyclic graph of graphes

The function `graph2dag(mygraph)` uses Tarjan to transform a graph into a direct acyclic graph (DAG):

`` graph2dag(const digraph<N>&) -> digraph<digraph<N>>``

The nodes of the resulting DAG are themselves graphs representing the strongly connected components of the input graph.

### Parallelize

Provided the input graph is a DAG, the function `parallelize()` transforms the input graph into a sequence of parallel nodes

``parallelize(const digraph<N>&) -> vector<vector<N>>``

### Serialize

Provided the input graph is a DAG, the function `serialize()` transforms the input graph into a vector of nodes

``serialize(const digraph<N>&) -> vector<N>``

### Map nodes

The function `mapnodes()` creates a copy of the input graph in which each node is transformed by the function `f()`. Existing connections in the input graph are preserved in the resulting graph.

``mapnodes(const digraph<N>&, f:N->M) -> digraph<M>``

### Map connections

The function `mapconnections()` creates a copy of the input graph in which only the connections that satisfy the predicate `f()` are kept.

``mapconnections(const digraph<N>&, f:(N,N,int)->bool) -> digraph<N>``

### Cut high-value connections

The function `cut()` creates a copy of the input graph in which all connections of value >= `d` are eliminated.

``cut(const digraph<N>&, d) -> digraph<N>``

### Split graph

The function `splitgraph()` splits a graph `G` into two subgraphs `L` and `R` according to a predicate `left()`. The nodes satisfying the predicate are copied into `L`, the others into `R`. The connections are kept, unless they concern nodes that are not in the same subgraph.

``splitgraph(const digraph<N>& G, function<bool(const N&)> left, digraph<N>& L, digraph<N>& R)``

# Digraph

## Very simple C++ directed graph library

### Digraph Info

⭐ Stars 23
🔗 Source Code github.com
🕒 Last Update a year ago
🕒 Created 5 years ago
🐞 Open Issues 2
➗ Star-Issue Ratio 12
😎 Author grame-cncm