Graph classes (Python)


PGraph: graphs for Python

A Python Robotics Package QUT Centre for Robotics Open Source

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This Python package allows the manipulation of directed and non-directed graphs. Also supports embedded graphs. It is suitable for graphs with thousands of nodes.

road network

from pgraph import *
import json

# load places and routes
with open('places.json', 'r') as f:
    places = json.loads(
with open('routes.json', 'r') as f:
    routes = json.loads(

# build the graph
g = UGraph()

for name, info in places.items():
    g.add_vertex(name=name, coord=info["utm"])

for route in routes:
    g.add_edge(route[0], route[1], cost=route[2])

# plan a path from Hughenden to Brisbane
p = g.path_Astar('Hughenden', 'Brisbane')
g.plot(block=False) # plot it
g.highlight_path(p)  # overlay the path

Properties and methods of the graph

Graphs belong to the class UGraph or DGraph for undirected or directed graphs respectively. The graph is essentially a container for the vertices.

  • g.add_vertex() add a vertex

  • g.n the number of vertices

  • g is an iterator over vertices, can be used as for vertex in g:

  • g[i] reference a vertex by its index or name

  • g.add_edge() connect two vertices

  • g.edges() all edges in the graph

  • g.plot() plots the vertices and edges

  • the number of graph components, 1 if fully connected

  • g.component(v) the component that vertex v belongs to

  • g.path_BFS() breadth-first search

  • g.path_Astar() A* search

  • g.adjacency() adjacency matrix

  • g.Laplacian() Laplacian matrix

  • g.incidence() incidence matrix

Properties and methods of a vertex

Vertices belong to the class UVertex (for undirected graphs) or DVertex (for directed graphs), which are each subclasses of Vertex.

  • v.coord the coordinate vector for embedded graph (optional)
  • the name of the vertex (optional)
  • v.neighbours() is a list of the neighbouring vertices
  • v1.samecomponent(v2) predicate for vertices belonging to the same component

Vertices can be named and referenced by name.

Properties and methods of an edge

Edges are instances of the class Edge. Edges are not referenced by the graph object, each edge references a pair of vertices, and the vertices reference the edges. For a directed graph only the start vertex of an edge references the edge object, whereas for an undirected graph both vertices reference the edge object.

  • e.cost cost of edge for planning methods
  • vertex on edge e that is not v
  • e.v1, e.v2 the two vertices that define the edge e

Modifying a graph

  • g.remove(v) remove vertex v
  • e.remove() remove edge e

Subclasing pgraph classes

Consider a user class Foo that we would like to connect using a graph overlay, ie. instances of Foo becomes vertices in a graph.

  • Have it subclass either DVertex or UVertex depending on graph type
  • Then place instances of Foo into the graph using add_vertex and create edges as required
class Foo(UVertex):
  # foo stuff goes here
f1 = Foo(...)
f2 = Foo(...)

g = UGraph() # create a new undirected graph

f1.connect(f2, cost=3)
for f in f1.neighbours():
    # say hi to the neighbours

Under the hood

The key objects and their interactions are shown below.

data structures

MATLAB version

This is a re-engineered version of PGraph.m which ships as part of the Spatial Math Toolbox for MATLAB. This class is used to support bundle adjustment, pose-graph SLAM and various planners such as PRM, RRT and Lattice.

The Python version was designed from the start to work with directed and undirected graphs, whereas directed graphs were a late addition to the MATLAB version. Semantics are similar but not identical. In particular the use of subclassing rather than references to user data is encouraged.

CRICOS No. 00213J