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PageRank Research Sandbox

Summary

Explores ranking strategies via deterministic graphs, sampling approximations, and convergence diagnostics.

Problem

Ranking nodes consistently requires understanding convergence and runtime trade-offs across graph sizes.

Approach

Built deterministic test graphs, compared sampling-based approximations to iterative solvers, and logged runtime/contraction diagnostics for each teleport probability.

Highlights

• Designed deterministic graphs to validate convergence and teleport parameters.
• Logged runtime profiles for sampling vs. iterative methods with the same seed.
• Captured diagnostics (residuals, norm) so deviations are easy to inspect.

Results

Iterative runtime (10k nodes)

TBD

Profiling under way.

Sampling variance

TBD

Will add confidence intervals.

Evaluation

Iterative PageRank vs. sampling-based approximation

Multiple deterministic graphs (purpose-built)

Baseline: Uniform teleport probability

Limitations

Sampling variance needs quantification before production adoption.
Real-world link graphs might have heavier tails than the deterministic test sets.

In progress: adding benchmarks and visuals.

Trade-offs

• Sampling approximations run faster but introduce variance; iterative solves are stable but compute-heavy for large graphs.
• Deterministic graphs simplify analysis but need to be mapped back to noisy real-world link data.

Next improvements

• Surface convergence tolerance vs. runtime so downstream teams can pick the right dial.
• Compare telemetry on actual link graphs when resources allow.