Small extensions of the Bellman-Ford routines in NetworkX, primarily for convenience (https://networkx.github.io).

## Project description

This package provides a few small extensions of the Bellman-Ford routines in NetworkX, primarily for convenience.

## Installation

bellmanford is available on PyPI:

```pip install bellmanford
```

## Usage

### bellman_ford

```length, nodes, negative_cycle = bellman_ford(G, source, target, weight='weight')
```

Compute shortest path and shortest path lengths between a source node and target node in weighted graphs using the Bellman-Ford algorithm.

#### Parameters

• G : NetworkX graph
• pred : dict - Keyed by node to predecessor in the path
• dist : dict - Keyed by node to the distance from the source
• source: node label - Source node
• target: node label - Target node
• weight : string - Edge data key corresponding to the edge weight

#### Returns

• length : numeric - Length of a negative cycle if one exists; otherwise length of a shortest path.
• nodes : list - Nodes in a negative edge cycle (in order) if one exists; otherwise nodes in a shortest path.
• negative_cycle : bool - True if a negative edge cycle exists, otherwise False.

#### Examples

```>>> import networkx as nx
>>> G = nx.path_graph(5, create_using = nx.DiGraph())
>>> bf.bellman_ford(G, source=0, target=4)
(3, [1, 2, 3, 4], False)
```

### negative_edge_cycle

```length, nodes, negative_cycle = negative_edge_cycle(G, weight='weight')
```

If there is a negative edge cycle anywhere in G, returns True. Also returns the total weight of the cycle and the nodes in the cycle.

#### Parameters

• G : NetworkX graph
• weight : string, optional (default = 'weight') - Edge data key corresponding to the edge weight

#### Returns

• length : numeric - Length of a negative edge cycle if one exists, otherwise None.
• nodes : list - Nodes in a negative edge cycle (in order) if one exists, otherwise None.
• negative_cycle : bool - True if a negative edge cycle exists, otherwise False.

#### Examples

```>>> import networkx as nx
>>> import bellmanford as bf
>>> G = nx.cycle_graph(5, create_using = nx.DiGraph())
>>> print(bf.negative_edge_cycle(G))
(None, [], False)
>>> G['weight'] = -7
>>> print(bf.negative_edge_cycle(G))
(-3, [4, 0, 1, 2, 3, 4], True)
```

## Project details 0.2.1 0.1.2

This version 0.1.1 0.1