.. index:: single: weighted_graph_protocol
.. _weighted_graph_protocol/0:

.. rst-class:: right

**protocol**

``weighted_graph_protocol``
===========================

Protocol for weighted graph predicates, extending the common graph protocol with weighted edge operations.

| **Availability:** 
|    ``logtalk_load(graphs(loader))``

| **Author:** Paulo Moura
| **Version:** 1:0:0
| **Date:** 2026-02-25

| **Compilation flags:**
|    ``static``


| **Extends:**
|    ``public`` :ref:`graph_protocol <graph_protocol/0>`

| **Remarks:**
|    (none)

| **Inherited public predicates:**
|     :ref:`graph_protocol/0::add_edges/3`  :ref:`graph_protocol/0::add_vertex/3`  :ref:`graph_protocol/0::add_vertices/3`  :ref:`graph_protocol/0::all_pairs_min_paths/2`  :ref:`graph_protocol/0::all_pairs_min_predecessors/2`  :ref:`graph_protocol/0::breadth_first_order/3`  :ref:`graph_protocol/0::delete_edges/3`  :ref:`graph_protocol/0::delete_vertex/3`  :ref:`graph_protocol/0::delete_vertices/3`  :ref:`graph_protocol/0::depth_first_order/3`  :ref:`graph_protocol/0::edges/2`  :ref:`graph_protocol/0::empty/1`  :ref:`graph_protocol/0::has_path/3`  :ref:`graph_protocol/0::is_bipartite/1`  :ref:`graph_protocol/0::is_complete/1`  :ref:`graph_protocol/0::is_sparse/1`  :ref:`graph_protocol/0::max_path/5`  :ref:`graph_protocol/0::min_distances/3`  :ref:`graph_protocol/0::min_path/5`  :ref:`graph_protocol/0::min_predecessors/3`  :ref:`graph_protocol/0::neighbors/3`  :ref:`graph_protocol/0::new/1`  :ref:`graph_protocol/0::new/2`  :ref:`graph_protocol/0::new/3`  :ref:`graph_protocol/0::number_of_edges/2`  :ref:`graph_protocol/0::number_of_vertices/2`  :ref:`graph_protocol/0::path/3`  :ref:`graph_protocol/0::reachable/3`  :ref:`graph_protocol/0::vertices/2`  

.. contents::
   :local:
   :backlinks: top

Public predicates
-----------------

.. index:: edge/4
.. _weighted_graph_protocol/0::edge/4:

``edge/4``
^^^^^^^^^^

True iff there is an edge between ``Vertex1`` and ``Vertex2`` with weight ``Weight`` in ``Graph``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``edge(Vertex1,Vertex2,Weight,Graph)``
| **Mode and number of proofs:**
|    ``edge(+vertex,+vertex,?number,+graph)`` - ``zero_or_one``


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

.. index:: add_edge/5
.. _weighted_graph_protocol/0::add_edge/5:

``add_edge/5``
^^^^^^^^^^^^^^

Adds a weighted edge between ``Vertex1`` and ``Vertex2`` with weight ``Weight``.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``add_edge(Graph,Vertex1,Vertex2,Weight,NewGraph)``
| **Mode and number of proofs:**
|    ``add_edge(+graph,+vertex,+vertex,+number,-graph)`` - ``one``


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

.. index:: delete_edge/5
.. _weighted_graph_protocol/0::delete_edge/5:

``delete_edge/5``
^^^^^^^^^^^^^^^^^

Deletes the weighted edge between ``Vertex1`` and ``Vertex2``. Unifies ``Weight`` with the weight of the deleted edge. The graph is unchanged if the edge does not exist.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``delete_edge(Graph,Vertex1,Vertex2,Weight,NewGraph)``
| **Mode and number of proofs:**
|    ``delete_edge(+graph,+vertex,+vertex,?number,-graph)`` - ``one``


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

.. index:: wneighbors/3
.. _weighted_graph_protocol/0::wneighbors/3:

``wneighbors/3``
^^^^^^^^^^^^^^^^

Unifies ``WNeighbors`` with a list of ``NeighborVertex-Weight`` pairs for the neighbors of ``Vertex``. Fails if ``Vertex`` is not in the graph.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``wneighbors(Vertex,Graph,WNeighbors)``
| **Mode and number of proofs:**
|    ``wneighbors(+vertex,+graph,-list(pair))`` - ``zero_or_one``


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

.. index:: min_path_bellman_ford/5
.. _weighted_graph_protocol/0::min_path_bellman_ford/5:

``min_path_bellman_ford/5``
^^^^^^^^^^^^^^^^^^^^^^^^^^^

Finds the minimum cost path from ``Vertex1`` to ``Vertex2`` using the Bellman-Ford algorithm. Supports negative edge weights and fails if no path exists or if a reachable negative cycle makes the optimum undefined.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``min_path_bellman_ford(Vertex1,Vertex2,Graph,Path,Cost)``
| **Mode and number of proofs:**
|    ``min_path_bellman_ford(+vertex,+vertex,+graph,-list(vertex),-number)`` - ``zero_or_one``


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

.. index:: has_negative_cycle/1
.. _weighted_graph_protocol/0::has_negative_cycle/1:

``has_negative_cycle/1``
^^^^^^^^^^^^^^^^^^^^^^^^

True iff ``Graph`` contains a negative-weight cycle.

| **Compilation flags:**
|    ``static``

| **Template:**
|    ``has_negative_cycle(Graph)``
| **Mode and number of proofs:**
|    ``has_negative_cycle(+graph)`` - ``zero_or_one``


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

Protected predicates
--------------------

(no local declarations; see entity ancestors if any)

Private predicates
------------------

(no local declarations; see entity ancestors if any)

Operators
---------

(none)