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graph-theory

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A simple graph library

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# graph-theory
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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](https://github.com/root-11/graph-theory/blob/master/examples/readme.md).

---------------------------
Install:

pip install graph-theory

Upgrade:

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

Testing:

pytest tests

---------------------------
Import:

import Graph
    g = Graph()

import Graph3d
    g3d = Graph3D()

---------------------------

Modules:

| 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](examples/solving%20search%20problems.ipynb) |
| + | + | `g.critical_path_minimize_for_slack()` | returns graph with artificial dependencies that minimises slack. | [Example](examples/solving%20search%20problems.ipynb)|
| + | + | `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. ||

## FAQ

| 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),` ` (1,b,4),(b,2,0)]` | Explicit is better than implicit. |
| multiple values on an edge | `g.add_edge(1,2,{'a':3, 'b':4})` | Have two graphs `g_a.add_edge(1,2,3)` `g_b.add_edge(1,2,4)` | 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|

## Credits:

- Arturo Soucase for packaging and testing. 
- Peter Norvig for inspiration on TSP from [pytudes](https://github.com/norvig/pytudes/blob/master/ipynb/TSP.ipynb).
- 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.
- Sappique for discovering bugs in `__eq__`, `copy` and `has_cycles`.
- joshinils for discovering bug where `graph.edges(from_node=0)` was interpreted as `False`.

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