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# `altgraph.Graph` — Basic directional graphs

The module `altgraph.Graph` provides a class `Graph` that represents a directed graph with N nodes and E edges.

class `altgraph.Graph.``Graph`([edges])

  Constructs a new empty `Graph` object. If the optional edges parameter is supplied, updates the graph by adding the specified edges.

  All of the elements in edges should be tuples with two or three elements. The first two elements of the tuple are the source and destination node of the edge, the optional third element is the edge data. The source and destination nodes are added to the graph when the aren’t already present.

## Node related methods

`Graph.``add_node`(node[, node_data])

  Adds a new node to the graph if it is not already present. The new node must be a hashable object.

  Arbitrary data can be attached to the node via the optional node_data argument.

  Note

  the node also won’t be added to the graph when it is present but currently hidden.

`Graph.``hide_node`(node)

  Hides a node from the graph. The incoming and outgoing edges of the node will also be hidden.

  Raises `altgraph.GraphError` when the node is not (visible) node of the graph.

`Graph.``restore_node`(node)

  Restores a previously hidden node. The incoming and outgoing edges of the node are also restored.

  Raises `altgraph.GraphError` when the node is not a hidden node of the graph.

`Graph.``restore_all_nodes`()

  Restores all hidden nodes.

`Graph.``number_of_nodes`()

  Return the number of visible nodes in the graph.

`Graph.``number_of_hidden_nodes`()

  Return the number of hidden nodes in the graph.

`Graph.``node_list`()

  Return a list with all visible nodes in the graph.

`Graph.``hidden_node_list`()

  Return a list with all hidden nodes in the graph.

`altgraph.Graph.``node_data`(node)

  Return the data associated with the node when it was added.

`Graph.``describe_node`(node)

  Returns node, the node’s data and the lists of outgoing and incoming edges for the node.

  Note

  the edge lists should not be modified, doing so can result in unpredicatable behavior.

`Graph.``__contains__`(node)

  Returns True iff node is a node in the graph. This method is accessed through the in operator.

`Graph.``__iter__`()

  Yield all nodes in the graph.

`Graph.``out_edges`(node)

  Return the list of outgoing edges for node

`Graph.``inc_edges`(node)

  Return the list of incoming edges for node

`Graph.``all_edges`(node)

  Return the list of incoming and outgoing edges for node

`Graph.``out_degree`(node)

  Return the number of outgoing edges for node.

`Graph.``inc_degree`(node)

  Return the number of incoming edges for node.

`Graph.``all_degree`(node)

  Return the number of edges (incoming or outgoing) for node.

## Edge related methods

`Graph.``add_edge`(head_id, tail_id[, edge data[, create_nodes]])

  Adds a directed edge from head_id to tail_id. Arbitrary data can be added via edge_data. When create_nodes is True (the default), head_id and tail_id will be added to the graph when the aren’t already present.

`Graph.``hide_edge`(edge)

  Hides an edge from the graph. The edge may be unhidden at some later time.

`Graph.``restore_edge`(edge)

  Restores a previously hidden edge.

`Graph.``restore_all_edges`()

  Restore all edges that were hidden before, except for edges referring to hidden nodes.

`Graph.``edge_by_node`(head, tail)

  Return the edge ID for an edge from head to tail, or `None` when no such edge exists.

`Graph.``edge_by_id`(edge)

  Return the head and tail of the edge

`Graph.``edge_data`(edge)

  Return the data associated with the edge.

`Graph.``head`(edge)

  Return the head of an edge

`Graph.``tail`(edge)

  Return the tail of an edge

`Graph.``describe_edge`(edge)

  Return the edge, the associated data, its head and tail.

`Graph.``number_of_edges`()

  Return the number of visible edges.

`Graph.``number_of_hidden_edges`()

  Return the number of hidden edges.

`Graph.``edge_list`()

  Returns a list with all visible edges in the graph.

`Graph.``hidden_edge_list`()

  Returns a list with all hidden edges in the graph.

## Graph traversal

`Graph.``out_nbrs`(node)

  Return a list of all nodes connected by outgoing edges.

`Graph.``inc_nbrs`(node)

  Return a list of all nodes connected by incoming edges.

`Graph.``all_nbrs`(node)

  Returns a list of nodes connected by an incoming or outgoing edge.

`Graph.``forw_topo_sort`()

  Return a list of nodes where the successors (based on outgoing edges) of any given node apear in the sequence after that node.

`Graph.``back_topo_sort`()

  Return a list of nodes where the successors (based on incoming edges) of any given node apear in the sequence after that node.

`Graph.``forw_bfs_subgraph`(start_id)

  Return a subgraph consisting of the breadth first reachable nodes from start_id based on their outgoing edges.

`Graph.``back_bfs_subgraph`(start_id)

  Return a subgraph consisting of the breadth first reachable nodes from start_id based on their incoming edges.

`Graph.``iterdfs`(start[, end[, forward]])

  Yield nodes in a depth first traversal starting at the start node.

  If end is specified traversal stops when reaching that node.

  If forward is True (the default) edges are traversed in forward direction, otherwise they are traversed in reverse direction.

`Graph.``iterdata`(start[, end[, forward[, condition]]])

  Yield the associated data for nodes in a depth first traversal starting at the start node. This method will not yield values for nodes without associated data.

  If end is specified traversal stops when reaching that node.

  If condition is specified and the condition callable returns False for the associated data this method will not yield the associated data and will not follow the edges for the node.

  If forward is True (the default) edges are traversed in forward direction, otherwise they are traversed in reverse direction.

`Graph.``forw_bfs`(start[, end])

  Returns a list of nodes starting at start in some bread first search order (following outgoing edges).

  When end is specified iteration stops at that node.

`Graph.``back_bfs`(start[, end])

  Returns a list of nodes starting at start in some bread first search order (following incoming edges).

  When end is specified iteration stops at that node.

`Graph.``get_hops`(start[, end[, forward]])

  Computes the hop distance to all nodes centered around a specified node.

  First order neighbours are at hop 1, their neigbours are at hop 2 etc. Uses `forw_bfs()` or `back_bfs()` depending on the value of the forward parameter.

  If the distance between all neighbouring nodes is 1 the hop number corresponds to the shortest distance between the nodes.

  Typical usage:

      >>> print graph.get_hops(1, 8)
      >>> [(1, 0), (2, 1), (3, 1), (4, 2), (5, 3), (7, 4), (8, 5)]
      # node 1 is at 0 hops
      # node 2 is at 1 hop
      # ...
      # node 8 is at 5 hops

## Graph statistics

`Graph.``connected`()

  Returns True iff every node in the graph can be reached from every other node.

`Graph.``clust_coef`(node)

  Returns the local clustering coefficient of node.

  The local cluster coefficient is the proportion of the actual number of edges between neighbours of node and the maximum number of edges between those nodes.

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