nographs 0.0.1.dev1

Algorithms for graphs, that are computed and/or adapted on the fly

NoGraphs simplifies the analysis of graphs that can not or should not be fully computed, stored or adapted, e.g. infinite graphs, large graphs and graphs with expensive computations. (Here, the word graph denotes the thing with vertices and edges, not with diagrams.)

The approach: Graphs are computed and/or adapted in application code on the fly (when needed and as far as needed). Also, the analysis and the reporting of results by the library happens on the fly (when, and as far as, results can already be derived).

Think of it as graph analysis - the lazy (evaluation) way.

Feature overview

• Algorithms: DFS, BFS, topological search, Dijkstra, A* and MST.

• Flexible graph notion: Infinite directed multigraphs with loops and attributes (this includes multiple adjacency, cycles, self-loops, directed edges, weighted edges and edges with application specific attributes). Your vertices can be nearly anything. Currently, all algorithms are limited to locally finite graphs (i.e., a vertex has only finitely many outgoing edges).

• Results: Reachability, depth, distance, paths and trees. Paths can be calculated with vertices or edges or attributed edges and can be iterated in both directions.

• Flexible API: It eases operations like graph pruning, graph product and graph abstraction, the computation of search-aware graphs and traversals of vertex equivalence classes on the fly. It is even possible to replace some of the internal data structures and to interfere with them during the search.

• Implementation: Pure Python (>=3.9). It introduces no further dependencies. Runtime and memory performance have been goals.

• Source: Available here.

• Licence: MIT.

Documentation

• The homepage of the project and its documentation can be found here

• The installation is described here.

• The tutorial explains how the library can be used and contains many examples.

• The API reference documents the classes, functions, signatures and types of the library.

Example

Our graph is directed, weighted and has infinitely many edges. These edges are defined in application code by the following function. For a vertex i (here: an integer) as the first of two parameters, it yields the edges that start at i as tuples (end_vertex, edge_weight). What a strange graph - we do not know how it looks like…

>>> def next_edges(i, _):
...     j = (i + i // 6) % 6
...     yield i + 1, j * 2 + 1
...     if i % 2 == 0:
...         yield i + 6, 7 - j
...     elif i > 5:
...         yield i - 6, 1

We would like to find out the distance of vertex 5 from vertex 0, i.e., the minimal necessary sum of edge weights of any path from 0 to 5, and (one of) the shortest paths from 0 to 5.

We do not know which part of the graph is necessary to look at in order to find the shortest path and to make sure, it is really the shortest. So, we use the traversal strategy TraversalShortestPaths of NoGraphs. It implements the well-known Dijkstra graph algorithm in the lazy evaluation style of NoGraphs.

>>> import nographs as nog
>>> traversal = nog.TraversalShortestPaths(next_edges)

We ask NoGraphs to traverse the graph starting at vertex 0, to calculate paths while doing so, and to stop when visiting vertex 5.

>>> traversal.start_from(0, build_paths=True).go_to(5)
5

The state data of this vertex visit contains our result:

>>> traversal.distance
24
>>> traversal.paths[5]
(0, 1, 2, 3, 4, 10, 16, 17, 11, 5)

We learn that we need to examine the graph at least till vertex 17 to find the shortest path from 0 to 5. It is not easy to see that from the definition of the graph…

A part of the graph, the vertices up to 41, is shown in the following picture. Arrows denote directed edges. The edges in red show shortest paths from 0 to other vertices.

Welcome to NoGraphs!