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Graph Peripherality #11898

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Title: Add graph peripherality algorithms for computing peripheral and far nodes

Description:

This pull request introduces new algorithms to compute the peripheral and far nodes in a weighted graph. It includes the implementation of the Floyd-Warshall algorithm for all-pairs shortest paths and functions to calculate eccentricity and harmonic closeness centrality. The code is well-documented, includes comprehensive type hints, and contains doctests for various graph scenarios to ensure correctness.

  • Add an algorithm?
  • Fix a bug or typo in an existing algorithm?
  • Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
  • Documentation change?

Checklist:

  • I have read CONTRIBUTING.md.
  • This pull request is all my own work -- I have not plagiarized.
  • I know that pull requests will not be merged if they fail the automated tests.
  • This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
  • All new Python files are placed inside an existing directory.
  • All filenames are in all lowercase characters with no spaces or dashes.
  • All functions and variable names follow Python naming conventions.
  • All function parameters and return values are annotated with Python type hints.
  • All functions have doctests that pass the automated testing.
  • All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
  • If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

Commit:

Initial Commit: Add algorithms to determine peripheral and farthest nodes in a weighted graph

  • Implemented Floyd-Warshall algorithm to calculate all-pairs shortest paths,
    supporting positive edge weights for weighted graphs.
  • Added functions to identify peripheral and far nodes:
    • find_peripheral_node: Determines the node with maximal eccentricity.
    • find_far_node: Finds the node with maximal farness, summing shortest-path distances.
  • Included error handling for non-positive edge weights, with appropriate ValueError raising.
  • Developed extensive test cases using doctests:
    • Covered single-node, fully connected, sparse, cyclic, directed acyclic, and
      disconnected graphs.
    • Validated handling of edge cases including zero and negative weights.
  • Ensured code meets PEP 8 standards and passed all lint checks with ruff.
  • Provided detailed module-level docstring with explanations of algorithms,
    complexity, and example applications.

@jeffreyyancey
Initial Commit: Add algorithms to determine peripheral and farthest n…
a5f9b2e 
…odes in a weighted graph

- Implemented Floyd-Warshall algorithm to calculate all-pairs shortest paths,
  supporting positive edge weights for weighted graphs.
- Added functions to identify peripheral and far nodes:
  - `find_peripheral_node`: Determines the node with maximal eccentricity.
  - `find_far_node`: Finds the node with maximal farness, summing shortest-path distances.
- Included error handling for non-positive edge weights, with appropriate ValueError raising.
- Developed extensive test cases using doctests:
  - Covered single-node, fully connected, sparse, cyclic, directed acyclic, and
    disconnected graphs.
  - Validated handling of edge cases including zero and negative weights.
- Ensured code meets PEP 8 standards and passed all lint checks with `ruff`.
- Provided detailed module-level docstring with explanations of algorithms,
  complexity, and example applications.

This commit provides foundational functionality for graph-theoretical analysis
and sets up for future expansions or integrations.
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