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A graph library

Project description


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A simple graph library...
... A bit like networkx, just without the overhead...
... similar to graph-tool, without the Python 2.7 legacy...
... with code that you can explain to your boss...

Detailed tutorial evolving in the examples section.

Latest feature:

2022/01/04 new feature: Graph.distance_map, which allows the user to compute
           the distance from a number of starts and ends as simulated annealing map.
2022/01/04 new generation of the traffic jam solver.
2021/12/12 shortest path now accepts keyword `avoids`, which allows the user
           to declare nodes which cannot be a part of the path.
           This feature has no impact on performance.


pip install graph-theory


pip install graph-theory --upgrade --no-cache


import Graph
g = Graph()  

import Graph3d
g3d = Graph3D()


module description
from graph import Graph, Graph3D Elementary methods (see basic methods below) for Graph and Graph3D.
from graph import ... All methods available on Graph (see table below)
from graph.assignment_problem import ... solvers for assignment problem, the Weapons-Target Assignment Problem, ...
from graph.hash import ... graph hash functions: graph hash, merkle tree, flow graph hash
from graph.random import ... graph generators for random, 2D and 3D graphs.
from graph.transshipment_problem import ... solvers for the transshipment problem
from graph.traffic_scheduling_problem import ... solvers for the traffic jams (and slide puzzle)
from graph.visuals import ... methods for creating matplotlib plots
from graph.finite_state_machine import ... finite state machine

All module functions are available from Graph and Graph3D (where applicable).

Graph Graph3D methods returns example
+ + a in g assert if g contains node a
+ + g.add_node(n, [obj]) adds a node (with a pointer to object obj if given)
+ + g.copy() returns a shallow copy of g
+ + g.node(node1) returns object attached to node 1
+ + g.del_node(node1) deletes node1 and all it's edges
+ + g.nodes() returns a list of nodes
+ + len(g.nodes()) returns the number of nodes
+ + g.nodes(from_node=1) returns nodes with edges from node 1
+ + g.nodes(to_node=2) returns nodes with edges to node 2
+ + g.nodes(in_degree=2) returns nodes with 2 incoming edges
+ + g.nodes(out_degree=2) returns nodes with 2 outgoing edges
+ + g.add_edge(1,2,3) adds edge to g for vector (1,2) with value 3
+ + g.edge(1,2) returns value of edge between nodes 1 and 2
+ + g.edge(1,2,default=3) returns default=3 if edge(1,2) doesn't exist.
similar to d.get(key, 3)
+ + g.del_edge(1,2) removes edge between nodes 1 and 2
+ + g.edges() returns a list of edges
+ + len(g.edges()) returns the number of edges
+ + g.edges(path=[path]) returns a list of edges (along a path if given).
+ + same_path(p1,p2) compares two paths to determine if they contain same sequences
ex.: [1,2,3] == [2,3,1]
+ + g.edges(from_node=1) returns edges outgoing from node 1
+ + g.edges(to_node=2) returns edges incoming to node 2
+ + g.from_dict(d) updates the graph from a dictionary
+ + g.to_dict() returns the graph as a dictionary
+ + g.from_list(L) updates the graph from a list
+ + g.to_list() return the graph as a list of edges
+ + g.shortest_path(start,end [, memoize, avoids]) returns the distance and path for path with smallest edge sum
If memoize=True, sub results are cached for faster access if repeated calls.
If avoids=set(), then these nodes are not a part of the path.
+ + g.shortest_path_bidirectional(start,end) returns distance and path for the path with smallest edge sum using bidrectional search.
+ + g.is_connected(start,end) determines if there is a path from start to end
+ + g.breadth_first_search(start,end) returns the number of edges and path with fewest edges
+ + g.breadth_first_walk(start,end) returns a generator for a BFS walk
+ + g.degree_of_separation(n1,n2) returns the distance between two nodes using BFS
+ + g.distance_map(starts,ends, reverse) returns a dictionary with the distance from any start to any end (or reverse)
+ + g.network_size(n1, degree_of_separation) returns the nodes within the range given by degree_of_separation
+ + g.topological_sort(key) returns a generator that yields node in order from a non-cyclic graph.
+ + g.critical_path() returns the distance of the critical path and a list of Tasks. Example
+ + g.critical_path_minimize_for_slack() returns graph with artificial dependencies that minimises slack. Example
+ + g.phase_lines() returns a dictionary with the phase_lines for a non-cyclic graph.
+ + g.sources(n) returns the source_tree of node n
+ + g.depth_first_search(start,end) returns path using DFS and backtracking
+ + g.depth_scan(start, criteria) returns set of nodes where criteria is True
+ + g.distance_from_path(path) returns the distance for path.
+ + g.maximum_flow(source,sink) finds the maximum flow between a source and a sink
+ + g.maximum_flow_min_cut(source,sink) finds the maximum flow minimum cut between a source and a sink
+ + g.minimum_cost_flow(inventory, capacity) finds the total cost and flows of the capacitated minimum cost flow.
+ + g.solve_tsp() solves the traveling salesman problem for the graph.
Available methods: 'greedy' (default) and 'bnb
+ + g.subgraph_from_nodes(nodes) returns the subgraph of g involving nodes
+ + g.is_subgraph(g2) determines if graph g2 is a subgraph in g
+ + g.is_partite(n) determines if graph is n-partite
+ + g.has_cycles() determines if there are any cycles in the graph
+ + g.components() returns set of nodes in each component in g
+ + g.same_path(p1,p2) compares two paths, returns True if they're the same
+ + g.adjacency_matrix() returns the adjacency matrix for the graph
+ + g.all_pairs_shortest_paths() finds the shortest path between all nodes
+ + g.minsum() finds the node(s) with shortest total distance to all other nodes
+ + g.minmax() finds the node(s) with shortest maximum distance to all other nodes
+ + g.shortest_tree_all_pairs() finds the shortest tree for all pairs
+ + g.has_path(p) asserts whether a path p exists in g
+ + g.all_simple_paths(start,end) finds all simple paths between 2 nodes
+ + g.all_paths(start,end) finds all combinations of paths between 2 nodes
- + g3d.distance(n1,n2) returns the spatial distance between n1 and n2
- + g3d.n_nearest_neighbour(n1, [n]) returns the n nearest neighbours to node n1
- + g3d.plot() returns matplotlib plot of the graph.


want to... doesn't work... do instead... ...but why?
have multiple edges between two nodes Graph(from_list=[(1,2,3), (1,2,4)] Add dummy nodes
[(1,a,3), (a,2,0),
Explicit is better than implicit.
multiple values on an edge g.add_edge(1,2,{'a':3, 'b':4}) Have two graphs
Most graph algorithms don't work with multiple values
do repeated calls to shortest path g.shortest_path(a,b) is slow Use g.shortest_path(a,b,memoize=True) instead memoize uses bidirectional search and caches sub-results along the shortest path for future retrievals


  • Arturo Soucase for packaging and testing.
  • Peter Norvig for inspiration on TSP from pytudes.
  • Harry Darby for the mountain river map.
  • Kyle Downey for depth_scan algorithm.
  • Ross Blandford for munich firebrigade centre -, traffic jam - and slide puzzle - test cases.
  • Avi Kelman for type-tolerant search, and a number of micro optimizations.
  • Joshua Crestone for all simple paths test.
  • CodeMartyLikeYou for detecting a bug in @memoize
  • Tom Carroll for detecting the bug in del_edge and inspiration for topological sort.

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