# Graph tutorial¶

## Creating a graph¶

Let us start by creating a graph, which is a collection of vertices (aka nodes) and edges. We will use the default graph which uses integers to represent vertices and edges.

>>> import jgrapht
>>> g = jgrapht.create_graph(directed=True, weighted=True, allowing_self_loops=False, allowing_multiple_edges=False)


This is the most general call. Sensible defaults are also provided, thus someone can create a graph simply by calling jgrapht.create_graph().

Vertices are added by calling method Graph.add_vertex(). The user can provide explicitly the vertex identifier as a parameter:

>>> g.add_vertex(0)


It is also possible to let the graph create automatically one:

>>> g.add_vertex()


The newly created vertex identifier is returned by the call, in order to be used when adding edges. Multiple vertices can also be added using any iterable.

>>> g.add_vertices_from([2, 3])


## Vertex set¶

Now the graph contains 4 vertices. You can find how many vertices the graph contains using,

>>> len(g.vertices)


The property Graph.vertices returns the set of vertices, which is also helpful in order to iterate over them.

>>> for v in g.vertices:
>>>     print ('Vertex {}'.format(v))


Edges are pairs of vertices, either ordered or unordered, depending on whether the graph is directed or undirected. In the default graph, edges are represented using integers. These edges are automatically created by the graph.

>>> e1 = g.add_edge(0, 1)


The call above creates a new edge from vertex 0 to vertex 1 and returns its representation. Multiple edges can be created in one go by using,

>>> g.add_edges_from([(0, 2), (1, 2)])


The method returns the newly created edges. Note also that it is possible to provide the edge representation explicitly using,

>>> g.add_edge(0, 1, edge=5)


In the example above we explicitly request to add edge 5 in the graph. If the graph already contains such an edge, the graph is not altered.

## Edge information¶

Using the edge we can retrieve the underlying information of the edge such as its source and its target. While in undirected graphs there is no source or target, we use the same naming scheme to keep a uniform interface. This is very helpful in order to implement algorithms which work both in directed and undirected graphs. Let us now read the edge source and target from the graph,

>>> print ('Edge {} has source {}'.format(e1, g.edge_source(e1)))
>>> print ('Edge {} has target {}'.format(e1, g.edge_target(e1)))


Graphs can be weighted or unweighted. In the case of unweighted graphs, method Graph.get_edge_weight() always returns 1.0 . This allows algorithms designed for weighted graphs to also work in unweighted ones. Here is how to read the weight of an edge,

>>> print ('Edge {} has weight {}'.format(e1, g.get_edge_weight(e1)))


If the graph is weighted, the edge weight can be adjusted using method Graph.set_edge_weight(). The user can also provide the weight directly when adding the edge to the graph,

>>> e2 = g.add_edge(1, 3, weight=10.0)


Care must be taken to not try to adjust the weight if the graph is unweighted. In such a case a ValueError is raised.

## Edge set¶

Edges can be iterated using the set returned by Graph.edges,

>>> for e in g.edges:
>>>     print ('Edge {} has source {}'.format(e, g.edge_source(e)))
>>>     print ('Edge {} has target {}'.format(e, g.edge_target(e)))


The same effect can be performed using the helper method Graph.edge_tuple() which returns a tuple containing the source, the target, and the weight of the edge. If the graph is unweighted, the weight returned is always 1.0.

>>> for e in g.edges:
>>>     print ('Edge {}'.format(g.edge_tuple(e)))


Finding the number of edges can be performed by executing,

>>> len(g.edges)


## Graph types¶

The type of the graph can be queried during runtime using Graph.type which returns instances of GraphType. This allows algorithms to alter their behavior based on the actual graph that they are running on. The following properties can be queried,

>>> g.type.directed
>>> g.type.undirected
>>> g.type.weighted
>>> g.type.allowing_multiple_edges
>>> g.type.allowing_self_loops
>>> g.type.modifiable


Now that we have seen a little bit how to create graphs, let us discuss what it means to contain self-loops or multiple-edges:

• self-loops are edges which start at a vertex v and end at the same vertex v,

• multiple-edges are edges which have the exact same endpoints.

Some algorithms are able to tolerate this, others do not. Thus, it is important to read the documentation of each algorithm in order to check whether such cases are tolerated. Some algorithms raise a ValueError in case they detect that they are running on a graph that contains either self-loops or multiple-edges.

If the graph is constructed to not allow self-loops and/or multiple-edges, an attempt to add such an edge will also raise a ValueError.

Finally, unmodifiable graphs are graphs which cannot be altered anymore. They can be constructed using either function as_unmodifiable() or by using some other graph factory function, such as factory for sparse graphs, which we will discuss later on.

## BFS implementation example¶

Let us implement a breadth-first search using JGraphT in order to get familiar with the library:

def bfs(graph, source):
queue = []
visited = set()

queue.append(source)