Common Graph Operations

Many common graph operations map to simple operators in graphi. Unless parameters are needed, builtin operations usually suffice. For example, the outdegree of a node is simply its number of outgoing edges, i.e.

out_degree = len(graph[node])

in a directed graph. Since graphi makes heavy use of data views (instead of copies), this has optimal performance.

Pythonic Graph Operations

Nodes of a graph

Graphs behave like a set with regard to nodes. Note that removing a node also invalidates all its edges and their values.

graph[a] = True

graph.add(a)

graph.discard(a)

Safely add or remove a node a from graph.

del graph[a]

Remove a node a from graph.

a in graph

Whether there is a node a in graph.

list(graph)

iter(graph)

for a in graph:

List/iterate/traverse all nodes in graph .

len(graph)

The number of nodes in the graph.

Edges and values of a graph

Graphs special-case edges: an edge is a secondary key, being the value to nodes and the key to edge values.

Edge[a:b] in graph

Whether there is an edge from node a to node b in graph.

Loop[a] in graph

Edge[a:a] in graph

Whether there is a loop from node a to itself in graph.

list(graph[a])

iter(graph[a])

for b in graph[a]:

List/iterate/loop all nodes for which there is an edge from node a, i.e. its neighbours.

len(graph[a])

The number of outgoing edges of node a, i.e. its outdegree.

Edge values of a graph

Graphs behave similar to a dict, tying values to edges. Note that removing a node also invalidates all its edges and their values.

graph[a:b] = w

graph[Edge[a:b]] = w

Add an edge from node a to node b with value w.

Pythonic Graph Types

By default, every graph is a weighted, directed graph - edges are oriented from start to end node and have one edge value. However, other graph types can be created with standard language features.

graph[a:b] = True

Add an edge from node a to node b with the primitive value True.

This creates an unweighted graph edge.

graph[a:b] = [w1, w2, w3, ...]

graph[a:b] = w1, w2, w3, ...

Add an edge from node a to node b with multiple values w1, w2, w3, ....

This creates a multigraph edge.