fix: DGraph.nc no longer loops forever; one components algorithm

[petercorke]

Summary

DGraph.nc loops forever for many directed graphs, and so does everything that asks for the components: component(), samecomponent() and plot(). This fixes it.

The bug

DGraph._graphcolor merged component labels with

while vlabel in merge:
    vlabel = merge[vlabel]

and the merge map can contain a cycle, so it never ends. The smallest case is a plain directed 4-cycle:

g = DGraph()
v = [g.add_vertex() for _ in range(4)]
for a, b in [(0, 2), (2, 1), (1, 3), (3, 0)]:
    g.add_edge(v[a], v[b])
g.nc        # never returns

A random 100-vertex, 300-edge digraph hangs too, and so does an acyclic one. It is the same on 0.6.5. The existing directed tests use tiny graphs that happen not to trigger it. I found it by timing plot() on a larger directed graph.

The fix

One algorithm, on Graph: a single O(V+E) traversal that follows each edge in either direction, replacing the two separate ones in UGraph and DGraph.

• Weakly connected components for a directed graph (direction ignored). That is what the existing tests and downstream code assume, and what the undirected algorithm already did; it is now stated in the docstrings.
• Components are numbered from 0 by the first vertex of each, in the order the vertices were added, for both kinds. (A directed graph's numbering was arbitrary.)

Also fixed in the same code

• Recomputed on every call. The graph's own dirty flag was never cleared, so once a graph had changed, every nc, component() and samecomponent() re-colored the whole graph. plot() asked for each component in turn. Now a call after no change is free.
• Vertex.label was None until something else had asked for the components (the tests had to prime it with g.nc). Reading it now finds them.
• A removed vertex no longer keeps its old label.
• The samecomponent() docstring was backwards: it said that for a directed graph "same component" implies a path and for an undirected graph it does not. It now says what a weak component is, with a -> c <- b as the example.

Tests

tests/test_components.py (36, both kinds), with a timeout guard so a hang fails rather than freezes the run, and expectations from hand-written cases or a union-find in the test:

• the 4-cycle, every call that asks for components, 30 random digraphs, and a 2,000-vertex digraph
• isolated vertices, paths, loops, parallel edges, labels in order, component() order, 0 to nc-1
• add/remove an edge or vertex changes the components, and nothing is recomputed when unchanged
• direction ignored (a -> c <- b), opposite edges, and DGraph agrees with UGraph on the same edges

On main, the 4-cycle tests hang and the label tests fail.

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[codacy-production]

Up to standards ✅

🟢 Issues 0 issues

Results:
0 new issues

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🟢 Metrics 59 complexity · 0 duplication

Metric	Results
Complexity	59
Duplication	0

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 95.88%. Comparing base (6bff60e) to head (aaf3e2e).

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #52      +/-   ##
==========================================
+ Coverage   95.37%   95.88%   +0.50%     
==========================================
  Files           3        3              
  Lines        1277     1238      -39     
==========================================
- Hits         1218     1187      -31     
+ Misses         59       51       -8     

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