Using the pagerankr Package

Introduction

The pagerankr package provides an SEO-focused toolkit for calculating, comparing, and analyzing PageRank scores from web crawl data. It handles the full pipeline from raw crawl exports (edge lists, redirect reports, nofollow annotations, indexability status) to actionable insights.

The package offers:

pagerank() – end-to-end wrapper for quick calculations
Modular functions – for granular control over each pipeline step
Model comparison – grid search, diff, and distribution metrics
What-if simulation – test link/redirect changes before production

All data manipulation uses base R. igraph powers the PageRank algorithm and graph-based redirect resolution. rurl handles URL canonicalization.

Installation

# install.packages("devtools")
devtools::install_github("bart-turczynski/pagerankr")

library(pagerankr)

Quick Start

edges <- data.frame(
  from = c(
    "example.com/home", "example.com/about",
    "example.com/blog", "example.com/blog"
  ),
  to = c(
    "example.com/about", "example.com/home",
    "example.com/home", "example.com/about"
  )
)

pr <- pagerank(edges)
print(pr)
#>                  node_name pagerank
#> 1 http://example.com/about    0.475
#> 2  http://example.com/blog    0.050
#> 3  http://example.com/home    0.475

Screaming Frog crawl exports

pagerankr can score a Screaming Frog crawl directly when you export:

Internal: All for node facts, redirects, canonicals, and indexability.
All Inlinks or All Outlinks for link observations.

The package keeps those contracts separate. Internal: All is node-only and is never treated as an edge list. The link export preserves raw observations, but only Type == "Hyperlink" rows with valid source and destination become graph edges. Resource, canonical, hreflang, and other link-row types stay available through import diagnostics.

bundle <- screaming_frog_bundle(
  internal = "internal_all.csv",
  links = "all_outlinks.csv",
  link_export_kind = "all_outlinks"
)

pr <- pagerank_screaming_frog(bundle)

summary(bundle)
attr(pr, "screaming_frog_import")
attr(pr, "transition_audit")

By default, all graph-eligible Hyperlink edges are scored. HTML/rendered origin filtering, placement selection, and placement-derived weights are opt-in scoring policy:

pagerank_screaming_frog(
  bundle,
  accepted_placements = c("nav", "content"),
  link_origins = c("html", "html_rendered"),
  placement_weights = c(nav = 2, content = 1)
)

For large crawls, the import adapters read only the columns used by the stable contract. If an export is degraded, missing optional columns become typed NA values and are reported in diagnostics; missing required columns error early. The bundle provenance includes detected column aliases and contract version, so production pipelines should pin the expected contract_version.

Redirect Resolution

Basic redirect handling

edges <- data.frame(
  from = c("A", "B", "C"),
  to = c("B", "C", "D")
)
redirects <- data.frame(
  from = c("B", "C"),
  to = c("B_new", "C_new")
)

# resolve_redirects() applies redirect rules to an edge list
resolved <- resolve_redirects(edges, redirects)
print(resolved)
#>    from    to
#> 1     A B_new
#> 2 B_new C_new
#> 3 C_new     D

Redirect chains are resolved transitively: if A redirects to B and B redirects to C, then A resolves to C.

Conflicting redirects

Crawl data often has the same URL redirecting to different targets. Use duplicate_from_policy to control the behavior:

redirects_conflict <- data.frame(
  from = c("old", "old", "old"),
  to = c("target_A", "target_B", "target_B")
)

# "most_frequent" picks the most common target
edges_simple <- data.frame(from = "X", to = "old")
resolve_redirects(edges_simple, redirects_conflict,
  duplicate_from_policy = "most_frequent"
)
#>   from       to
#> 1    X target_B

Available policies: strict (default, errors on conflict), first_wins, last_wins, most_frequent, prune_source, resolve_if_consistent.

Redirect loops

Redirect cycles (A -> B -> C -> A) are detected via strongly connected components. Use loop_handling to control behavior:

edges_loop <- data.frame(from = "X", to = "A")
redirects_loop <- data.frame(
  from = c("A", "B", "C", "D"),
  to = c("B", "C", "A", "E")
)

# "prune_loop" removes cycle edges; linear redirects still work
resolved <- resolve_redirects(edges_loop, redirects_loop,
  loop_handling = "prune_loop"
)
print(resolved)
#>   from to
#> 1    X  A

Available policies: error (default), prune_loop, break_arrow (keeps the highest in-degree node as sink).

Standalone link resolution

Use resolve_links() to apply redirects and deduplicate without computing PageRank – useful for inspecting the resolved graph:

edges <- data.frame(
  from = c("A", "A", "B"),
  to = c("B", "B", "C")
)
redirects <- data.frame(from = "B", to = "B_final")

resolve_links(edges, redirects, clean_urls = FALSE)
#>      from      to
#> 1       A B_final
#> 2 B_final       C

Nofollow Handling

pagerankr provides three explicit propagation policies for links marked nofollow:

"evaporate" (the default) keeps each nofollow link as an outgoing slot. It consumes its weighted share of the source page’s budget, but that share reaches a sink rather than the target.
"drop" removes nofollow links before allocating the outgoing budget. They consume no slots, and followed links divide the full budget.
"keep" follows the links normally, so their targets receive their shares.

These are package modeling choices; they are not claims about a search engine’s current implementation.

edges <- data.frame(
  from = c("Hub", "Hub", "Hub"),
  to = c("A", "B", "C"),
  nofollow = c(FALSE, FALSE, TRUE)
)

# "evaporate": PR splits 3 ways, C's share vanishes
pr_evap <- pagerank(edges,
  nofollow_col = "nofollow",
  nofollow_action = "evaporate",
  clean_edge_urls = FALSE
)
print(pr_evap)
#>   node_name   pagerank
#> 1         A 0.10586618
#> 2         B 0.10586618
#> 3       Hub 0.08249313

# "drop": nofollow edges removed, PR splits only among followed links
pr_drop <- pagerank(edges,
  nofollow_col = "nofollow",
  nofollow_action = "drop",
  clean_edge_urls = FALSE
)
print(pr_drop)
#>   node_name  pagerank
#> 1         A 0.3701299
#> 2         B 0.3701299
#> 3       Hub 0.2597403

Indexability

noindex pages

pagerankr assumes that the ranked corpus consists of indexed documents. Under this indexed-corpus assumption, a noindex page is outside the ranked corpus. It may receive authority through inlinks, but cannot redistribute that authority within the indexed graph. The package therefore treats its outgoing links as nofollow for propagation, applying the selected nofollow_action: slot-consuming "evaporate", slot-removing "drop", or normally followed "keep".

This is strictly a pagerankr PageRank assumption. It does not mean that Google or another search engine defines noindex as an explicit nofollow directive. A noindex page can remain visible in the result to make its received authority auditable; hiding it would be an optional reporting choice, not a change required for correct propagation under this model.

edges <- data.frame(
  from = c("Home", "NoindexPage", "NoindexPage"),
  to = c("NoindexPage", "A", "B")
)

idx_status <- data.frame(
  url = "NoindexPage",
  indexability_status = "noindex"
)

pr <- pagerank(edges,
  indexability_df = idx_status,
  clean_edge_urls = FALSE
)
print(pr)
#>     node_name pagerank
#> 1        Home   0.0500
#> 2 NoindexPage   0.0925

robots.txt blocked pages

A robots.txt-blocked page receives inbound PageRank but cannot pass it outbound (Google can’t see the links). The PR is either trapped or vanishes:

edges <- data.frame(
  from = c("Home", "Blocked", "A"),
  to = c("Blocked", "A", "Home")
)

idx_status <- data.frame(
  url = "Blocked",
  indexability_status = "Blocked by robots.txt"
)

# "trap": blocked page keeps its PR (visible in results)
pr_trap <- pagerank(edges,
  indexability_df = idx_status,
  robots_blocked_action = "trap",
  clean_edge_urls = FALSE
)
print(pr_trap)
#>   node_name pagerank
#> 1         A   0.0500
#> 2   Blocked   0.8575
#> 3      Home   0.0925

# "vanish": blocked page removed from results
pr_vanish <- pagerank(edges,
  indexability_df = idx_status,
  robots_blocked_action = "vanish",
  clean_edge_urls = FALSE
)
print(pr_vanish)
#>   node_name pagerank
#> 1         A   0.0500
#> 2      Home   0.0925

Weighted Edges

Pass a weight_col to use link weights (e.g., number of links, link position scores) in the PageRank calculation:

edges <- data.frame(
  from = c("A", "A", "B"),
  to = c("B", "C", "C"),
  weight = c(3, 1, 1)
)

pr <- pagerank(edges, weight_col = "weight", clean_edge_urls = FALSE)
print(pr)
#>   node_name  pagerank
#> 1         A 0.1907714
#> 2         B 0.3123882
#> 3         C 0.4968403

Duplicate from -> to rows are a separate modeling choice. By default, pagerank() uses duplicate_edge_policy = "collapse": repeated links from one source page to the same destination become one binary destination edge, matching the common textbook PageRank convention and preserving legacy results. Use duplicate_edge_policy = "aggregate" when duplicate rows carry additive weights that should be summed, or "count_instances" when each repeated link slot should increase the transition probability to that target.

Domain Filtering

filter_links_by_domain() scopes edge lists by domain, useful for separating internal vs. external links:

edges <- data.frame(
  from = c(
    "example.com/a", "example.com/b",
    "other.com/c"
  ),
  to = c(
    "example.com/b", "other.com/d",
    "example.com/a"
  )
)

# Keep only internal links
internal <- filter_links_by_domain(edges, keep_domains = "example.com")
print(internal)
#>            from            to
#> 1 example.com/a example.com/b

HITS hub and authority

hits() computes Kleinberg’s HITS hub and authority scores over the same cleaned, redirect/canonical-folded, domain-filtered, deduplicated link graph as pagerank(). Because both share the identity pipeline, you can join hub, authority, and PageRank on node_name directly.

The two scores reinforce each other: a good authority is pointed to by good hubs, and a good hub points to good authorities. Formally, with adjacency matrix A, authority is the dominant eigenvector of A^T A and hub is the dominant eigenvector of A A^T.

edges <- data.frame(
  from = c("A", "A", "B"),
  to = c("B", "C", "C")
)

# A only points out (pure hub); C is only pointed to (pure authority).
hits(edges, clean_edge_urls = FALSE)
#>   node_name      hub authority
#> 1         A 1.000000  0.000000
#> 2         B 0.618034  0.618034
#> 3         C 0.000000  1.000000

Scores are scaled so each maximum is 1 (scale = TRUE, the conventional HITS reporting). HITS already captures both directions of authority flow, so there is no reverse flag, and the PageRank-only forward-flow devices (nofollow evaporation, indexability transforms, the TIPR teleport prior) are not exposed.

Whole-graph caveat. Kleinberg’s original HITS ran on a small, query-focused base set of pages. hits() runs on the full (or domain-filtered) site graph pagerankr assembles, so treat the scores as site-wide structural centralities rather than query-relevance scores.

SALSA hub and authority

salsa() computes Lempel & Moran’s (2001) SALSA hub and authority scores over the same identity pipeline as pagerank() and hits(), so all three join on node_name. SALSA is the stochastic cousin of HITS: it replaces the mutual-reinforcement iteration with two random walks on the bipartite hub/authority graph, so the scores are stationary distributions rather than the dominant eigenvectors HITS returns. On a connected graph this collapses to a degree-based closed form — authority = d_in / W, hub = d_out / W, where W is the edge count — so no eigenvector iteration is needed.

edges <- data.frame(
  from = c("A", "A", "B"),
  to = c("B", "C", "C")
)

# A only points out (pure hub); C is only pointed to (pure authority).
salsa(edges, clean_edge_urls = FALSE)
#>   node_name       hub authority
#> 1         A 0.6666667        NA
#> 2         B 0.3333333 0.3333333
#> 3         C        NA 0.6666667

Each side is a probability distribution that sums to 1. When the graph splits into several weakly connected components, each component’s scores are renormalized within the component and then reweighted by that component’s share of the side (Lempel & Moran 2001, Proposition 6) — required so scores stay comparable across orphan page clusters.

Coverage differs from PageRank. The hub side holds only pages with outlinks and the authority side only pages with inlinks, so hub is NA for a pure sink and authority is NA for a pure source (an isolate is NA for both). v1 is unweighted; like hits() the forward-flow devices (nofollow, indexability, the TIPR prior, reverse) are not exposed. As with hits(), these are site-wide structural centralities, a documented site-graph adaptation of the original focused-subgraph algorithm.

Model Comparison

Comparing two models

edges <- data.frame(
  from = c("A", "B", "C", "D"),
  to = c("B", "C", "D", "A")
)

pr_85 <- pagerank(edges, damping = 0.85, clean_edge_urls = FALSE)
pr_90 <- pagerank(edges, damping = 0.90, clean_edge_urls = FALSE)

diff <- compare_pagerank(pr_85, pr_90, label_a = "d=0.85", label_b = "d=0.90")
print(diff)
#>   node_name pagerank_d=0.85 pagerank_d=0.90        delta   pct_change
#> 1         B            0.25            0.25 5.551115e-17 2.220446e-14
#> 2         A            0.25            0.25 2.775558e-17 1.110223e-14
#> 3         C            0.25            0.25 2.775558e-17 1.110223e-14
#> 4         D            0.25            0.25 2.775558e-17 1.110223e-14
#>   rank_d=0.85 rank_d=0.90 rank_delta
#> 1           4           1          3
#> 2           1           1          0
#> 3           1           1          0
#> 4           1           1          0
cat("\nCorrelation summary:\n")
#> 
#> Correlation summary:
print(attr(diff, "summary"))
#> $spearman_rho
#> [1] NA
#> 
#> $mean_abs_delta
#> [1] 3.469447e-17
#> 
#> $nodes_gained
#> [1] 0
#> 
#> $nodes_lost
#> [1] 0

Parameter grid search

Run PageRank across multiple parameter combinations to find the most informative model:

edges <- data.frame(
  from = c("A", "A", "B", "C"),
  to = c("B", "C", "C", "A")
)

grid <- auto_grid(damping = c(0.75, 0.85, 0.95))
results <- pagerank_grid(edges, params_grid = grid, clean_edge_urls = FALSE)

# Analyse distribution metrics across the grid
analysis <- analyze_pagerank_grid(results)
print(analysis)
#>       model_id num_nodes pr_sum    pr_max   pr_gini pr_entropy pr_top10_share
#> 1 damping=0.75         3      1 0.3948718 0.1128205   1.070547      0.3948718
#> 2 damping=0.85         3      1 0.3973997 0.1217260   1.064454      0.3973997
#> 3 damping=0.95         3      1 0.3992712 0.1296778   1.058139      0.3992712

Distribution metrics

Standalone metrics for any PageRank vector:

pr <- pagerank(edges, clean_edge_urls = FALSE)
cat("Gini coefficient:", pr_gini(pr$pagerank), "\n")
#> Gini coefficient: 0.121726
cat("Entropy:", pr_entropy(pr$pagerank), "\n")
#> Entropy: 1.064454
cat("Top-1 share:", pr_top_k_share(pr$pagerank, k = 1), "\n")
#> Top-1 share: 1

Simulating Changes

A common SEO workflow is asking “what happens to PageRank if I add these links, remove those links, or implement these redirects?”

Adding links

site_links <- data.frame(
  from = c("Home", "Home", "About", "Blog"),
  to = c("About", "Blog", "Home", "Home")
)

impact <- simulate_changes(
  site_links,
  add_links_df = data.frame(
    from = "Blog", to = "About"
  ),
  clean_edge_urls = FALSE
)
print(impact)
#>   node_name pagerank_baseline pagerank_proposed       delta pct_change
#> 1     About         0.2567568         0.3333333  0.07657658  29.824561
#> 2      Home         0.4864865         0.4327485 -0.05373795 -11.046134
#> 3      Blog         0.2567568         0.2339181 -0.02283863  -8.895045
#>   rank_baseline rank_proposed rank_delta
#> 1             2             2          0
#> 2             1             1          0
#> 3             2             3         -1

Removing links

impact_remove <- simulate_changes(
  site_links,
  remove_links_df = data.frame(
    from = "Home", to = "Blog"
  ),
  clean_edge_urls = FALSE
)
print(impact_remove)
#>   node_name pagerank_baseline pagerank_proposed      delta pct_change
#> 1     About         0.2567568         0.4635135  0.2067568   80.52632
#> 2      Blog         0.2567568         0.0500000 -0.2067568  -80.52632
#> 3      Home         0.4864865         0.4864865  0.0000000    0.00000
#>   rank_baseline rank_proposed rank_delta
#> 1             2             2          0
#> 2             2             3         -1
#> 3             1             1          0

Simulating redirects

extended_links <- rbind(site_links, data.frame(
  from = "OldPage", to = "Home"
))

impact_redirect <- simulate_changes(
  extended_links,
  add_redirects_df = data.frame(
    from = "OldPage", to = "About"
  ),
  clean_edge_urls = FALSE
)
print(impact_redirect)
#>   node_name pagerank_baseline pagerank_proposed       delta pct_change
#> 1     About         0.2413851         0.2567568 0.015371622   6.368090
#> 2      Blog         0.2413851         0.2567568 0.015371622   6.368090
#> 3      Home         0.4797297         0.4864865 0.006756757   1.408451
#> 4   OldPage         0.0375000                NA          NA         NA
#>   rank_baseline rank_proposed rank_delta
#> 1             2             2          0
#> 2             2             2          0
#> 3             1             1          0
#> 4             4            NA         NA

Combined changes

impact_all <- simulate_changes(
  site_links,
  add_links_df = data.frame(
    from = "Blog", to = "About"
  ),
  remove_links_df = data.frame(
    from = "Home", to = "Blog"
  ),
  clean_edge_urls = FALSE
)
print(impact_all)
#>   node_name pagerank_baseline pagerank_proposed       delta pct_change
#> 1     About         0.2567568             0.475  0.21824324  85.000000
#> 2      Blog         0.2567568             0.050 -0.20675676 -80.526316
#> 3      Home         0.4864865             0.475 -0.01148649  -2.361111
#>   rank_baseline rank_proposed rank_delta
#> 1             2             1          1
#> 2             2             3         -1
#> 3             1             1          0

All pagerank() parameters (damping, nofollow, indexability, etc.) can be passed through simulate_changes() via ....

Convergence Controls and Damping Stability

pagerank() convergence controls

pagerank() delegates to igraph’s PageRank implementation. Two solvers are available via the algo argument:

"prpack" (default) — exact solver; ignores eps and niter.
"arpack" — iterative Arnoldi solver; required whenever you supply eps or niter. Passing either argument automatically switches the solver.

Key arguments:

Argument	Meaning
`algo`	`"prpack"` (default) or `"arpack"`
`eps`	L1 convergence tolerance (maps to ARPACK `options$tol`)
`niter`	Max iterations (maps to ARPACK `options$maxiter`)

Every result carries a "convergence" attribute — a pagerank_convergence object — that records the solver used, iteration count, and final L1 residual. Inspect it with attr(result, "convergence") or just print() the result.

Rule of thumb for iteration budget: ceiling(log10(eps) / log10(damping)) iterations are needed to reach tolerance eps at damping factor damping.

damping_sensitivity() and pagerank_stability()

damping_sensitivity() sweeps a vector of damping factors and returns one PageRank result per alpha:

damping_sensitivity(edge_list_df, alphas = c(0.75, 0.80, 0.85, 0.90, 0.95), ...)

pagerank_stability() wraps the sweep into a ready-to-read stability report:

pagerank_stability(
  edge_list_df,
  alphas     = c(0.75, 0.80, 0.85, 0.90, 0.95),
  reference  = 0.85,
  top_k      = 10,
  ...
)

It returns a data frame with one row per alpha and two comparison columns relative to the reference run:

spearman_rho — rank-order correlation across all URLs.
top_k_overlap — fraction of the top-k URLs shared with the reference.

The raw per-(url, alpha) scores are available via attr(stab, "sensitivity").

Worked example

toy_edges <- data.frame(
  from = c("A", "A", "B", "C", "C", "D", "E", "F"),
  to   = c("B", "C", "D", "D", "E", "F", "A", "A")
)

# Stability report: how sensitive are ranks to damping?
stab <- pagerank_stability(
  toy_edges,
  alphas            = c(0.75, 0.80, 0.85, 0.90, 0.95),
  reference         = 0.85,
  top_k             = 4,
  clean_edge_urls   = FALSE
)
print(stab)
#>   alpha spearman_rho mean_abs_delta top_k_overlap nodes_gained nodes_lost
#> 1  0.75            1    0.004359987             1            0          0
#> 2  0.80            1    0.002156580             1            0          0
#> 3  0.85            1    0.000000000             1            0          0
#> 4  0.90            1    0.002115985             1            0          0
#> 5  0.95            1    0.004196891             1            0          0
#>     algo iters iters_estimate     residual   tol converged n_nodes
#> 1 prpack    NA             25 8.326673e-17 0.001      TRUE       6
#> 2 prpack    NA             31 5.551115e-17 0.001      TRUE       6
#> 3 prpack    NA             43 9.714451e-17 0.001      TRUE       6
#> 4 prpack    NA             66 8.326673e-17 0.001      TRUE       6
#> 5 prpack    NA            135 1.110223e-16 0.001      TRUE       6

# Drill into raw per-(url, alpha) scores
head(attr(stab, "sensitivity"))
#>   url alpha      score iters iters_estimate     residual converged
#> 1   A  0.75 0.25210500    NA             25 8.326673e-17      TRUE
#> 2   D  0.75 0.19489846    NA             25 8.326673e-17      TRUE
#> 3   F  0.75 0.18784052    NA             25 8.326673e-17      TRUE
#> 4   B  0.75 0.13620604    NA             25 8.326673e-17      TRUE
#> 5   C  0.75 0.13620604    NA             25 8.326673e-17      TRUE
#> 6   E  0.75 0.09274393    NA             25 8.326673e-17      TRUE

At alpha values close to the reference the spearman_rho and top_k_overlap columns will be near 1; larger deviations flag URLs whose importance is damping-sensitive.

Topic-Sensitive PageRank

Standard PageRank treats every page as an equally likely teleport target. Topic-Sensitive PageRank (Haveliwala 2002, adapted here to a site graph) replaces that uniform prior with a cluster-biased one: the random surfer teleports only to pages that belong to a predefined topic cluster. The result is a family of per-topic authority scores — each score answers “how important is this page for visitors who care about topic X?” — plus a blended aggregate that weight-averages the individual topic vectors.

topic_sensitive_pagerank() is pure orchestration: it runs pagerank() once per topic with the appropriate seeded prior, then blends the results. Topic membership is supplied by the caller; it is never inferred from content.

Signature

topic_sensitive_pagerank(
  edge_list_df,
  topics,
  topic_weights      = NULL,
  topic_url_col      = "url",
  topic_weight_col   = "weight",
  ...
)

topics is a named list. Each element is either a character vector of seed URLs (equal-weight prior) or a data frame with URL and weight columns (custom prior).

Worked example

library(pagerankr)

# Small synthetic site: 7 pages, two rough topic clusters
edges <- data.frame(
  from = c("Home", "Home", "Blog", "Blog", "Shop", "Shop", "Docs"),
  to   = c("Blog", "Shop", "Post1", "Post2", "Item1", "Item2", "Guide1")
)

# Define two topics as named lists of seed URL vectors
topics <- list(
  content = c("Blog", "Post1", "Post2"),
  commerce = c("Shop", "Item1", "Item2")
)

tspr <- topic_sensitive_pagerank(
  edge_list_df    = edges,
  topics          = topics,
  clean_edge_urls = FALSE
)

print(tspr)
#>   node_name   content  commerce   blended
#> 1     Item1 0.0000000 0.3701299 0.1850649
#> 2     Item2 0.0000000 0.3701299 0.1850649
#> 3     Post1 0.3701299 0.0000000 0.1850649
#> 4     Post2 0.3701299 0.0000000 0.1850649
#> 5      Blog 0.2597403 0.0000000 0.1298701
#> 6      Shop 0.0000000 0.2597403 0.1298701
#> 7      Docs 0.0000000 0.0000000 0.0000000
#> 8    Guide1 0.0000000 0.0000000 0.0000000
#> 9      Home 0.0000000 0.0000000 0.0000000

The returned data frame has one row per node and three score columns: content, commerce, and blended.

# Per-topic scores
tspr[, c("node_name", "content", "commerce")]
#>   node_name   content  commerce
#> 1     Item1 0.0000000 0.3701299
#> 2     Item2 0.0000000 0.3701299
#> 3     Post1 0.3701299 0.0000000
#> 4     Post2 0.3701299 0.0000000
#> 5      Blog 0.2597403 0.0000000
#> 6      Shop 0.0000000 0.2597403
#> 7      Docs 0.0000000 0.0000000
#> 8    Guide1 0.0000000 0.0000000
#> 9      Home 0.0000000 0.0000000

# Blended (equal topic weights by default)
tspr[, c("node_name", "blended")]
#>   node_name   blended
#> 1     Item1 0.1850649
#> 2     Item2 0.1850649
#> 3     Post1 0.1850649
#> 4     Post2 0.1850649
#> 5      Blog 0.1298701
#> 6      Shop 0.1298701
#> 7      Docs 0.0000000
#> 8    Guide1 0.0000000
#> 9      Home 0.0000000

topic_feeder_pagerank() answers the complementary question: which pages outside a cluster send the most PageRank authority into it? It operates on the reverse graph and seeds the teleport prior on the cluster itself. Use it when you want to find upstream link-building opportunities. See vignette("topic_feeder_pagerank") for a full walkthrough.

trustrank() is the unipolar variant: a single “trusted” seed set replaces the topic list, and there is no blending step. See vignette("trustrank").

GA4 Behavioral Transitions

GA4 event data captures how real users move through your site. The three functions in this section let you convert those signals into PageRank inputs without requiring a BigQuery connection — a synthetic events data frame is sufficient for local development.

Building transition counts with `ga4_page_transitions()`

ga4_page_transitions() walks each user-session in chronological order and emits one row per consecutive page-view pair. The result is a transition signal (observed navigation behavior), not a link-click signal, so it reflects where users actually go rather than where crawlable anchor tags point.

library(pagerankr)

# Minimal synthetic GA4 events data frame (no BigQuery required)
events <- data.frame(
  user_pseudo_id  = c("u1", "u1", "u1", "u2", "u2"),
  ga_session_id   = c(1L,   1L,   1L,   2L,   2L),
  page_location   = c("/home", "/blog", "/contact", "/home", "/pricing"),
  event_timestamp = c(1000L,  2000L,  3000L,  1000L,  2000L)
)

transitions <- ga4_page_transitions(
  events,
  user_id_col   = "user_pseudo_id",
  session_id_col = "ga_session_id",
  page_col       = "page_location",
  timestamp_col  = "event_timestamp"
)
print(transitions)
#>    from       to n
#> 1 /blog /contact 1
#> 2 /home    /blog 1
#> 3 /home /pricing 1
# Returns a data frame with columns: from, to, n

Smoothing sparse transitions with `smooth_transitions()`

Observed transition counts are often sparse — many source pages have very few sessions, making raw empirical shares unreliable. smooth_transitions() applies per-source Dirichlet smoothing toward a structural (crawl-graph) prior:

lambda_i = n_i / (n_i + k)

where n_i is the total outgoing transition count from source i and k controls how quickly low-traffic sources lean on the prior. Sources with fewer than min_support total outgoing transitions receive full prior weight (lambda_i = 0).

# Build a minimal structural prior from the same pages
structural <- data.frame(
  from = c("/home",    "/home",    "/blog"),
  to   = c("/blog",   "/pricing", "/contact"),
  n    = c(50L,        30L,        40L)
)

smoothed <- smooth_transitions(
  empirical_df   = transitions,
  structural_df  = structural,
  k              = 10,
  min_support    = 5,
  count_col      = "n",
  from_col       = "from",
  to_col         = "to",
  prob_col       = "prob"
)
print(smoothed)
#>    from       to prob empirical_count empirical_share structural_prior support
#> 1 /blog /contact  1.0               1             1.0              1.0       1
#> 2 /home    /blog  0.5               1             0.5              0.5       2
#> 3 /home /pricing  0.5               1             0.5              0.5       2
#>   lambda origin
#> 1      0   both
#> 2      0   both
#> 3      0   both
# empirical_df augmented with a `prob` column: smoothed per-source
# transition probabilities (each source sums to 1)

Converting entrances to a teleport vector with `ga4_entrance_teleport()`

ga4_entrance_teleport() turns landing-page entrance counts into a prior_df suitable for pagerank(prior_df = ...). This provides a proxy for external authority: pages users enter from search or direct traffic receive a higher reset probability during the random-surfer teleport step.

Note: entrance counts are not equivalent to backlink authority — they reflect observed user entry points, not link equity from external domains.

entrances <- data.frame(
  page_location = c("/home", "/blog", "/pricing", "/contact"),
  entrances     = c(120L,    80L,     40L,         10L)
)

prior <- ga4_entrance_teleport(
  entrances_df   = entrances,
  url_col        = "page_location",
  entrances_col  = "entrances",
  vertex_names   = NULL
)
print(prior)
#>        url weight
#> 1    /blog     80
#> 2 /contact     10
#> 3    /home    120
#> 4 /pricing     40
# Returns: url + weight data frame, ready for pagerank(prior_df = .)

End-to-end example

Combine all three steps: raw events → transition counts → smoothing → PageRank.

# 1. Extract transitions from synthetic events
trans <- ga4_page_transitions(
  events,
  user_id_col    = "user_pseudo_id",
  session_id_col = "ga_session_id",
  page_col       = "page_location",
  timestamp_col  = "event_timestamp"
)

# 2. Smooth against the structural prior
sm <- smooth_transitions(
  empirical_df  = trans,
  structural_df = structural,
  k             = 10,
  min_support   = 2,
  prob_col      = "prob"
)

# 3. Run PageRank using smoothed probabilities as edge weights
pr <- pagerank(
  sm,
  edge_from_col  = "from",
  edge_to_col    = "to",
  weight_col     = "prob",
  clean_edge_urls = FALSE
)
print(pr)
#>   node_name  pagerank
#> 1     /blog 0.2351000
#> 2  /contact 0.3648175
#> 3     /home 0.1649825
#> 4  /pricing 0.2351000

clean_edge_urls = FALSE is used throughout because the synthetic URLs are already normalized; set it to TRUE when feeding real GA4 page_location values that may contain query strings or fragments.

Function Reference

Function	Purpose
`pagerank()`	End-to-end: clean, resolve, compute
`hits()`	End-to-end HITS hub + authority on the same graph
`compute_hits()`	Low-level igraph HITS wrapper
`salsa()`	End-to-end SALSA hub + authority on the same graph
`compute_salsa()`	Low-level SALSA computational core
`resolve_links()`	Resolve redirects + deduplicate (no PR)
`simulate_changes()`	What-if: compare baseline vs. proposed
`compare_pagerank()`	Diff two PR results with rank shifts
`pagerank_grid()`	Run PR across parameter combinations
`auto_grid()`	Generate parameter grid
`analyze_pagerank_grid()`	Distribution metrics across a grid
`filter_links_by_domain()`	Scope edges by domain
`resolve_redirects()`	Apply redirects to an edge list
`clean_url_columns()`	Canonicalize URLs
`get_unique_edges()`	Deduplicate, handle self-loops
`drop_isolates()`	Include/exclude disconnected nodes
`compute_pagerank()`	Low-level igraph PR wrapper
`pr_gini()`	Gini coefficient of PR distribution
`pr_entropy()`	Entropy of PR distribution
`pr_top_k_share()`	Top-k concentration of PR
`damping_sensitivity()`	Sweep PageRank across a range of damping factors
`pagerank_stability()`	Alpha-stability report: rank correlation across damping grid
`topic_sensitive_pagerank()`	Per-topic personalized PageRank with blended scores
`topic_feeder_pagerank()`	Reverse-graph seeded PageRank: find pages that feed a target cluster
`trustrank()`	TrustRank: seed-biased PageRank from a trusted seed set
`trust_seed_prior()`	Build a teleport prior concentrated on trusted seed URLs (for trustrank)
`feeder_seed_prior()`	Build a teleport prior concentrated on cluster seed URLs (for topic_feeder_pagerank)
`align_prior_to_vertices()`	Align a prior/teleport weight data frame to the graph vertex set
`ga4_entrance_teleport()`	Entrance/landing-page counts as a teleport (reset) vector
`ga4_page_transitions()`	Consecutive-page-view transition counts from a GA4 BigQuery export
`smooth_transitions()`	Shrink sparse empirical transition shares toward structural prior
`transform_edge_weights()`	Per-source grouped edge weight transforms (emits transition_probability)
`transform_weights()`	Apply rank/log/zipf/percentile transforms to a numeric vector
`validate_edge_weights()`	Validate per-source weight totals and warn on anomalies
`screaming_frog_bundle()`	Compose Screaming Frog Internal:All + All Inlinks/Outlinks into a bundle
`screaming_frog_internal()`	Import Screaming Frog Internal: All export
`screaming_frog_links()`	Import Screaming Frog All Inlinks / All Outlinks export
`pagerank_screaming_frog()`	Score a screaming_frog_bundle via pagerank()
`resolve_canonical_urls()`	Resolve a URL vector through rel=canonical folds
`resolve_canonicals()`	Apply rel=canonical folds to an edge list
`resolve_folded_urls()`	Resolve a URL vector through redirects plus canonicals
`resolve_urls()`	Resolve a URL vector through a redirect map
`build_fold_map()`	Build a URL fold map from redirects and/or canonicals
`audit_canonicals()`	Diagnose rel=canonical fold coverage and conflicts
`audit_fold()`	Diagnose the redirect+canonical URL fold map
`audit_redirects()`	Diagnose redirect chains, loops, and conflicts
`aggregate_edges()`	Aggregate duplicate edges after URL folding with per-column semantics
`export_graph()`	Export graph + PageRank in graphml / dot / edgelist / pajek formats
`launch_pagerank_explorer()`	Launch the interactive Shiny PageRank explorer

Acknowledgments

pagerankr wraps igraph’s PageRank and HITS engines and implements a body of link-analysis research directly — PageRank (Brin & Page), HITS (Kleinberg), SALSA (Lempel & Moran), TrustRank (Gyöngyi, Garcia-Molina & Pedersen), and Topic-Sensitive PageRank (Haveliwala). URL handling is delegated to the sibling rurl package.

The full list of credits — prior art, dependencies, the research this code implements, and the data sources it serves — is in ACKNOWLEDGMENTS.md.

Bart Turczynski

2026-07-11

Introduction

Installation

Quick Start

Screaming Frog crawl exports

Redirect Resolution

Basic redirect handling

Conflicting redirects

Redirect loops

Standalone link resolution

Nofollow Handling

Indexability

noindex pages

robots.txt blocked pages

Weighted Edges

Domain Filtering

HITS hub and authority

SALSA hub and authority

Model Comparison

Comparing two models

Parameter grid search

Distribution metrics

Simulating Changes

Adding links

Removing links

Simulating redirects

Combined changes

Convergence Controls and Damping Stability

pagerank() convergence controls

damping_sensitivity() and pagerank_stability()

Worked example

Topic-Sensitive PageRank

Worked example

Distinguishing related functions

GA4 Behavioral Transitions

Building transition counts with ga4_page_transitions()

Smoothing sparse transitions with smooth_transitions()

Converting entrances to a teleport vector with ga4_entrance_teleport()

End-to-end example

Function Reference

Acknowledgments

Building transition counts with `ga4_page_transitions()`

Smoothing sparse transitions with `smooth_transitions()`

Converting entrances to a teleport vector with `ga4_entrance_teleport()`