Topic Feeder PageRank: what powers a content cluster

The question this answers

You have a content cluster you care about — say the AI-Agent product area — and you want to know which internal pages power it. Not “which AI-Agent page is the strongest” (that is an authority question), but the inverse: which pages funnel link authority into the cluster? Those are the internal hubs worth protecting, strengthening, or learning from when you build the next section.

topic_feeder_pagerank() answers exactly that. It is the reverse-graph sibling of topic_sensitive_pagerank().

Why it is not just re-reading PageRank

In PageRank, authority flows along link direction — linking to an important page does not make the linker important. So “the pages that feed the AI-Agent cluster” cannot be recovered from forward PageRank or from topic_sensitive_pagerank(): those rank pages by inflow (you are important because important pages point at you). Feeders are the opposite, an outflow notion (you are important because you point at the cluster).

Mechanically, topic_feeder_pagerank() seeds the random surfer’s teleport on the cluster and runs PageRank on the transposed graph (reverse = TRUE). Mass lands on the cluster, then walks backward along links, piling up on the pages that feed it. The damping factor attenuates that credit with link distance — a direct feeder beats a feeder-of-a-feeder. No new solver: it is a prior_df handed to pagerank(reverse = TRUE).

A worked example

edges <- data.frame(
  from = c(
    "/hub", "/hub", "/feeder", "/blog-ai", "/ai",
    "/footer", "/sports", "/footer"
  ),
  to = c(
    "/ai", "/ai-demo", "/ai", "/ai", "/ai-demo",
    "/ai", "/scores", "/sports"
  )
)

The AI-Agent cluster is c("/ai", "/ai-demo"). By construction /hub is the strongest feeder (it links to both cluster pages), /feeder and /blog-ai feed it once each, /footer links in too, and /sports / /scores are unrelated.

fr <- topic_feeder_pagerank(
  edges,
  seeds = c("/ai", "/ai-demo"),
  clean_edge_urls = FALSE,
  prior_verbose = FALSE
)
fr[, c("node_name", "pagerank", "prior_weight")]
#>   node_name  pagerank prior_weight
#> 1       /ai 0.3508772          0.5
#> 2  /ai-demo 0.2462296          0.5
#> 3      /hub 0.1792090          0.0
#> 4  /blog-ai 0.0745614          0.0
#> 5   /feeder 0.0745614          0.0
#> 6   /footer 0.0745614          0.0
#> 7   /scores 0.0000000          0.0
#> 8   /sports 0.0000000          0.0

Reading the output

prior_weight > 0 marks the cluster pages themselves — they carry the teleport mass directly, so a high score there is teleport, not a feeder signal.
The feeders are the high-pagerank rows with prior_weight == 0. Filter to those:

feeders <- fr[fr$prior_weight == 0, c("node_name", "pagerank")]
feeders
#>   node_name  pagerank
#> 3      /hub 0.1792090
#> 4  /blog-ai 0.0745614
#> 5   /feeder 0.0745614
#> 6   /footer 0.0745614
#> 7   /scores 0.0000000
#> 8   /sports 0.0000000

/hub tops the feeder list exactly as designed, and the off-topic /sports neighborhood earns no feeder credit.

Contrast with the forward (authority) view

Run topic_sensitive_pagerank() on the same cluster to see the difference in direction:

auth <- topic_sensitive_pagerank(
  edges,
  topics = list(ai_agent = c("/ai", "/ai-demo")),
  clean_edge_urls = FALSE,
  prior_verbose = FALSE
)
auth[, c("node_name", "ai_agent")]
#>   node_name  ai_agent
#> 1  /ai-demo 0.6491228
#> 2       /ai 0.3508772
#> 3  /blog-ai 0.0000000
#> 4   /feeder 0.0000000
#> 5   /footer 0.0000000
#> 6      /hub 0.0000000
#> 7   /scores 0.0000000
#> 8   /sports 0.0000000

The forward run concentrates score on the cluster and what it links onward to; the feeder run concentrates score on what points into the cluster. Use the forward view to find the cluster’s authorities, the feeder view to find its hubs.

Where it sits among the reverse-direction tools

pagerankr has three ways to look “backward” along links; pick by what you need:

pagerank(reverse = TRUE) — global outflow centrality (the inverse / CheiRank-style PageRank). “Which pages funnel authority outward anywhere on the site.” No cluster bias.
topic_feeder_pagerank() — the same idea, biased to a cluster: not “good hub in general” but “good hub for the AI-Agent cluster”. This is the one you want for the question at the top of this vignette.
hits() hubs — the eigenvector hub score (co-computed with authority). An outflow notion too, but with no teleport prior and no damped-surfer / dangling handling, so it answers a structurally different question.

Notes

Seed weights are an additive feeder budget: if two seed URLs fold onto the same vertex (redirect or canonical variants), their weights sum — consistent with the prior contract in pagerank() and align_prior_to_vertices().
Everything pagerank() accepts flows through ...: redirects, canonicals, URL cleaning, domain/host filtering, edge weights, and duplicate-edge policy. Cluster seeds are canonicalized and folded into the same vertex namespace as the edges before alignment.
Because the graph is always reversed, the forward-flow devices pagerank() rejects under reverse = TRUE (nofollow_action = "evaporate", indexability_df) are unavailable here too — use nofollow_action = "drop", the correct treatment of a nofollowed link for outflow. ```

Bart Turczynski