Add example for cycle detection (networkx#6560)

* Fix negative edge cycle function raising exception for empty graph and added relevant test function

* Unresolved change

* Added example script to visualize GOT network

* Added example script to visualize cycle detection

* Deleted got.py

* Minor tweaks to example.

* Update examples/algorithms/plot_cycle_detection.py

---------

Co-authored-by: Ross Barnowski <rossbar@caltech.edu>
Co-authored-by: Dan Schult <dschult@colgate.edu>

examples/algorithms/plot_cycle_detection.py

@@ -0,0 +1,29 @@
+"""
+===============
+Cycle Detection
+===============
+
+This example demonstrates the use of ``nx.find_cycle`` to find a single,
+arbitrary cycle in a graph.
+
+Other functions like ``nx.simple_cycles`` and ``nx.cycle_basis`` can be used to
+find all cycles or a cycle basis.
+"""
+import networkx as nx
+import matplotlib.pyplot as plt
+
+# Create a simple directed graph with a cycle
+G = nx.DiGraph([(1, 2), (2, 3), (3, 4), (4, 2), (3, 5), (3, 2), (1, 5)])
+
+# Draw the graph
+pos = nx.spring_layout(G, seed=8020)
+nx.draw(G, pos, with_labels=True)
+
+# The `orientation` parameter can be used to determine how directed edges are
+# treated and the reporting of edge direction in the cycle
+cycle = nx.find_cycle(G, orientation="original")
+print(cycle)
+
+# Highlight the cycle in red
+nx.draw_networkx_edges(G, pos, edgelist=cycle, edge_color="r", width=2)
+plt.show()