Add graph centrality algorithms to compute central and median nodes i…

[jeffreyyancey]

Describe your change:

Title: Add graph centrality algorithms for computing central and median nodes

Description:

This pull request introduces new algorithms to compute the central and median 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.

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

Checklist:

• [X] I have read CONTRIBUTING.md.
• [X] This pull request is all my own work -- I have not plagiarized.
• [X] I know that pull requests will not be merged if they fail the automated tests.
• [X] This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
• [X] All new Python files are placed inside an existing directory.
• [X] All filenames are in all lowercase characters with no spaces or dashes.
• [X] All functions and variable names follow Python naming conventions.
• [X] All function parameters and return values are annotated with Python type hints.
• [X] All functions have doctests that pass the automated testing.
• [X] 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".

[jeffreyyancey]

@imSanko Certainly.

---

Add graph centrality algorithms to compute central and median nodes in a graph

• Implement `floyd_warshall_algorithm` to compute all-pairs shortest paths using the Floyd-Warshall algorithm.
• Implement `find_central_and_median_node` to calculate eccentricity and harmonic closeness centrality for each node.
• Add helper functions:
  • `initialize_distance_matrix` for initializing the distance matrix and validating edge weights.
  • `calculate_node_centrality` for computing eccentricity and closeness of a single node.
• Include comprehensive module-level docstrings explaining:
  • The mathematical problem and its significance.
  • Descriptions of the algorithms used.
  • Pseudo-code for the Floyd-Warshall algorithm.
  • References to relevant Wikipedia articles.
• Add detailed type hints for all functions and variables to enhance code clarity and support static type checking.
• Refactor code to improve readability and maintainability:
  • Use descriptive variable names.
  • Introduce intermediate variables for complex expressions.
  • Add comments explaining key steps and computations.
• Ensure compliance with PEP 8 standards:
  • Adjust line lengths to not exceed 88 characters.
  • Reformat long strings and comments.
  • Fix issues identified by code linters like `ruff`.
• Handle exceptions properly:
  • Assign exception messages to variables before raising, adhering to best practices.
• Include doctests for various graph scenarios to verify correctness:
  • Single-node graphs.
  • Two-node graphs with positive weights.
  • Fully connected graphs.
  • Directed acyclic graphs (DAGs).
  • Disconnected graphs.
  • Graphs with zero or negative edge weights (raising exceptions).
  • Cyclic graphs.
  • Sparse graphs.

---

Please let me know if you have further questions.

[jeffreyyancey]

My branches seemed to have gotten crossed. I'll close this and recreate a new PR with the proper branch.

[imSanko]

@imSanko Certainly.

Add graph centrality algorithms to compute central and median nodes in a graph

• Implement floyd_warshall_algorithm to compute all-pairs shortest paths using the Floyd-Warshall algorithm.

• Implement find_central_and_median_node to calculate eccentricity and harmonic closeness centrality for each node.

• Add helper functions:

  • initialize_distance_matrix for initializing the distance matrix and validating edge weights.
  • calculate_node_centrality for computing eccentricity and closeness of a single node.

• Include comprehensive module-level docstrings explaining:

  • The mathematical problem and its significance.
  • Descriptions of the algorithms used.
  • Pseudo-code for the Floyd-Warshall algorithm.
  • References to relevant Wikipedia articles.

• Add detailed type hints for all functions and variables to enhance code clarity and support static type checking.

• Refactor code to improve readability and maintainability:

  • Use descriptive variable names.
  • Introduce intermediate variables for complex expressions.
  • Add comments explaining key steps and computations.

• Ensure compliance with PEP 8 standards:

  • Adjust line lengths to not exceed 88 characters.
  • Reformat long strings and comments.
  • Fix issues identified by code linters like ruff.

• Handle exceptions properly:

  • Assign exception messages to variables before raising, adhering to best practices.

• Include doctests for various graph scenarios to verify correctness:

  • Single-node graphs.
  • Two-node graphs with positive weights.
  • Fully connected graphs.
  • Directed acyclic graphs (DAGs).
  • Disconnected graphs.
  • Graphs with zero or negative edge weights (raising exceptions).
  • Cyclic graphs.
  • Sparse graphs.

Please let me know if you have further questions.

Make sure that the answers are plagiarism free and not AI Generated !