### Weighted graph algorithms with Python

#### Abstract

Python implementation of selected weighted graph data structures and algorithms is presented. The minimal graph interface is defined together with several classes implementing this interface. Graph nodes can be any hashable Python objects. Directed edges are instances of the Edge class. Graphs are instances of the Graph class. It is based on the adjacency-list representation, but with fast lookup of nodes and neighbors (dict-of-dict structure). Other implementations of this class are also included, for instance, the adjacency matrix representation (list-of-list structure). Multigraphs are instances of the Multigraph class.

In this work, many algorithms are implemented using a unified approach. There are separate classes and modules devoted to different algorithms. Three algorithms for finding a minimum spanning tree are implemented: the Boruvka's algorithm, the Prim's algorithm (three implementations), and the Kruskal's algorithm. Three algorithms for solving the single-source shortest path problem are implemented: the dag shortest path algorithm, the Bellman-Ford algorithm, and the Dijkstra's algorithm (two implementations). Two algorithms for solving all-pairs shortest path problem are implemented: the Floyd-Warshall algorithm and the Johnson's algorithm.

All algorithms were tested by means of the unittest module, the Python unit testing framework. Additional computer experiments were done in order to compare real and theoretical computational complexity. The source code is available from the public GitHub graphs-dict

repository.

In this work, many algorithms are implemented using a unified approach. There are separate classes and modules devoted to different algorithms. Three algorithms for finding a minimum spanning tree are implemented: the Boruvka's algorithm, the Prim's algorithm (three implementations), and the Kruskal's algorithm. Three algorithms for solving the single-source shortest path problem are implemented: the dag shortest path algorithm, the Bellman-Ford algorithm, and the Dijkstra's algorithm (two implementations). Two algorithms for solving all-pairs shortest path problem are implemented: the Floyd-Warshall algorithm and the Johnson's algorithm.

All algorithms were tested by means of the unittest module, the Python unit testing framework. Additional computer experiments were done in order to compare real and theoretical computational complexity. The source code is available from the public GitHub graphs-dict

repository.