.. 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)