implemented power of graph function under basic methods

src/sage/graphs/generic_graph.py

@@ -15746,6 +15746,47 @@ def distance_all_pairs(self, by_weight=False, algorithm=None,
  weight_function=weight_function,
  check_weight=check_weight)[0]
 
+ def power(self, k):
+ r"""
+ Compute the kth power graph of an unweighted graph based on shortest
+ distances between nodes using BFS.
+
+ INPUT:
+ - ``k`` -- integer; the maximum path length for considering edges in the power graph.
+
+ OUTPUT:
+ - The kth power graph based on shortest distances between nodes.
+
+ EXAMPLES:
+
+ Testing on undirected graphs::
+
+ sage: G = Graph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 5)])
+ sage: k = 2
+ sage: PG = G.power(k)
+ sage: PG.edges(sort=True, labels=False)
+ [(0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 2), (1, 3), (1, 4), (2, 0), (2, 1), (2, 3), (2, 4), (3, 0), (3, 1), (3, 2), (3, 4), (4, 0), (4, 1), (4, 2), (4, 3), (5, 4), (4, 5)]
+
+ Testing on directed graphs::
+
+ sage: G = DiGraph([(0, 1), (1, 2), (2, 3), (3, 0), (2, 4), (4, 5)])
+ sage: k = 3
+ sage: PG = g.power(k)
+ sage: PG.edges(sort=True, labels=False)
+ [(0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 2), (1, 3), (1, 4), (1, 5), (2, 0), (2, 1), (2, 3), (2, 4), (2, 5), (3, 0), (3, 1), (3, 2), (4, 5)]
+
+ """
+ from sage.graphs.graph import DiGraph, Graph
+
+ power_of_graph = DiGraph() if self.is_directed() else Graph()
+
+ for u in self:
+ for v in self.breadth_first_search(u, distance=k):
+ if u != v:
+ power_of_graph.add_edge(u, v)
+
+ return power_of_graph
+
  def girth(self, certificate=False):
  """
  Return the girth of the graph.