pagerank_stability: Report how stable a PageRank ranking is across damping...

In pagerankr: Modular Toolkit for PageRank Calculation

Report how stable a PageRank ranking is across damping factors

Description

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.

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').

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.

See Also

[damping_sensitivity()], [compare_pagerank()], [pagerank()] (the "Damping factor" section)

Examples

edges <- data.frame(
  from = c("A", "B", "C", "A", "D"),
  to = c("B", "C", "A", "C", "A")
)
stab <- pagerank_stability(edges, clean_edge_urls = FALSE)
print(stab)

# Drill into the per-(url, alpha) scores behind the summary.
head(attr(stab, "sensitivity"))

pagerankr documentation built on Oct. 1, 2026, 5:09 p.m.