Report how stable a PageRank ranking is across damping factors

Sweeps [pagerank()] over a grid of damping factors with [damping_sensitivity()] and compares each \(\alpha\)'s ranking against a reference \(\alpha\) with [compare_pagerank()], returning a one-row-per- \(\alpha\) stability summary. It answers the open question flagged in the "Damping factor" section of [pagerank()]: on *your* graph, how much does the ranking actually move as \(\alpha\) varies?

Usage

pagerank_stability(
  edge_list_df,
  alphas = c(0.75, 0.8, 0.85, 0.9, 0.95),
  reference = 0.85,
  top_k = 10,
  ...
)

Arguments

edge_list_df: A data frame representing the edge list, passed to every [pagerank()] call. (Named for consistency with the rest of the package; it is an edge list, not a constructed graph object.)
alphas: Numeric vector of damping factors to sweep, each strictly between 0 and 1. Default `c(0.75, 0.80, 0.85, 0.90, 0.95)`. Duplicate values are dropped.
reference: The baseline damping factor every other \(\alpha\) is compared against. A single number strictly between 0 and 1, default `0.85`. Included in the sweep automatically if not already in `alphas`.
top_k: Size of the top-scoring set used for the `top_k_overlap` churn metric. Positive integer, default `10`.
...: Additional arguments forwarded to [damping_sensitivity()] and on to [pagerank()] (e.g. `redirects_df`, `weight_col`, `algo`, `prior_df`). Passing `damping` is an error, since `alphas` drives the damping factor.

Value

A data frame with one row per swept \(\alpha\) (ascending), with columns:

`alpha`: The damping factor.
`spearman_rho`: Spearman rank correlation of this \(\alpha\)'s ranking against the reference, on their common nodes (`NA` if fewer than 3 common nodes).
`mean_abs_delta`: Mean absolute score difference vs the reference on common nodes.
`top_k_overlap`: Fraction in `[0, 1]` of the reference's top-`k` pages that are also in this \(\alpha\)'s top-`k` (1 = identical top set). The effective `k` shrinks to the node count on small graphs.
`nodes_gained`, `nodes_lost`: Nodes present at this \(\alpha\) but not the reference, and vice versa. Normally 0: varying \(\alpha\) changes scores, not the node set.
`algo`, `iters`, `iters_estimate`, `residual`, `tol`, `converged`, `n_nodes`: The per-\(\alpha\) convergence metadata carried over from [damping_sensitivity()].

The full per-(URL, \(\alpha\)) sensitivity frame from [damping_sensitivity()] is attached as the `"sensitivity"` attribute, and the `reference` and `top_k` used are attached as same-named attributes.

Details

A Spearman rank correlation near 1 across the whole grid means the choice of damping factor is immaterial for this graph — the conventional `0.85` is as good as any nearby value. A low correlation, or a top-\(k\) overlap well below 1, flags a graph whose ranking is genuinely \(\alpha\)-sensitive and worth investigating before trusting any single solve.

This is a thin orchestration layer: it performs no PageRank math of its own, delegating the solves to [damping_sensitivity()] and the rank-comparison statistics to [compare_pagerank()]. The `reference` factor is always included in the sweep (even if absent from `alphas`) so it can serve as the comparison baseline; its own row is a sanity anchor (`spearman_rho = 1`, `mean_abs_delta = 0`, `top_k_overlap = 1`).

Examples