Compute HITS hub and authority scores using igraph

Builds a directed graph from a processed edge list and computes Kleinberg's HITS hub and authority scores using `igraph::hits_scores()` (the non-deprecated successor of `igraph::hub_score()` / `igraph::authority_score()`). This is the low-level computational core; the high-level [hits()] wrapper runs the URL-cleaning, redirect/canonical folding, domain filtering, deduplication, and isolate handling identity pipeline first.

Usage

compute_hits(
  edge_list_df,
  vertices_df = NULL,
  from_col = "from",
  to_col = "to",
  vertex_col_name = "node_name",
  weight_col = NULL,
  weight_validation = c("error", "warning", "none"),
  scale = TRUE,
  pr_node_col = "node_name",
  hub_col = "hub",
  authority_col = "authority",
  ...
)

Arguments

edge_list_df: A data frame representing the processed edge list, with source/target columns (see `from_col`, `to_col`). NAs in those columns are omitted before graph construction.
vertices_df: An optional single-column data frame of node names defining the vertex set (e.g. to retain isolates). If `NULL` (default), the vertices are inferred from `edge_list_df`. The column name is given by `vertex_col_name`.
from_col, to_col: Names of the source/target columns in `edge_list_df`. Defaults `"from"` / `"to"`.
vertex_col_name: Name of the node column in `vertices_df`. Default `"node_name"`.
weight_col: Optional name of a numeric edge-weight column. Higher weights give an edge more influence in the hub/authority mutual reinforcement. If `NULL` (default), the graph is unweighted.
weight_validation: How invalid edge weights are handled when `weight_col` is supplied: `"error"` (default), `"warning"`, or `"none"`. See [validate_edge_weights()].
scale: Logical, passed to `igraph::hits_scores()`. When `TRUE` (default) each score vector is scaled so its maximum entry is `1`, the conventional HITS reporting convention. When `FALSE` the raw principal eigenvectors (unit Euclidean norm) are returned.
pr_node_col: Name for the node column in the output. Default `"node_name"` (kept consistent with [compute_pagerank()]).
hub_col, authority_col: Names for the hub and authority score columns in the output. Defaults `"hub"` / `"authority"`.
...: Additional arguments passed to `igraph::hits_scores()` (e.g. `options`).

Value

A data frame with three columns: the node name (named by `pr_node_col`) and the hub and authority scores (named by `hub_col` / `authority_col`). Returns an empty (zero-row) data frame with those columns when the graph has no vertices.

Details

## Matrix formulation

Let \(A\) be the adjacency matrix of the directed graph (\(A_{ij} = 1\) when page \(i\) links to page \(j\), or the edge weight when weighted). HITS computes two mutually reinforcing scores as the dominant eigenvectors:

**authority** is the dominant eigenvector of \(A^\top A\): a page is a good authority when it is pointed to by good hubs.
**hub** is the dominant eigenvector of \(A A^\top\): a page is a good hub when it points to good authorities.

`igraph::hits_scores()` solves these eigenproblems directly, so no separate direction flip is needed: authority is the inflow-oriented score and hub is the outflow-oriented score, both returned from a single call.

Examples