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Transform Edge Weights for PageRank

Source: R/transform_weights.R
transform_weights.Rd

Applies a transformation strategy to a numeric vector of edge weights before passing them to pagerank. Useful for converting link positions, click counts, or other raw signals into weights suitable for the PageRank random surfer model.

Usage

transform_weights(
  x,
  method = c("none", "rank_linear", "zipf", "log", "minmax", "percentile"),
  alpha = 1,
  offset = 1,
  floor_value = 0.01,
  descending = TRUE
)

Arguments

x

Numeric vector of raw weights (e.g., link positions on a page, GA4 click counts, or any positive numeric signal).

method

Character, the transformation strategy. One of:

"none"

Return x unchanged.

"rank_linear"

Convert to rank order (1 = highest value), then assign linearly decreasing weights: weight = (n - rank + 1) / n. Position 1 gets 1.0, position n gets 1/n.

"zipf"

Convert to rank order, then apply Zipf's law: weight = 1 / rank^alpha. Position 1 gets 1.0, position 2 gets 1/2^alpha, etc. Controlled by the alpha parameter (default 1).

"log"

Apply log(x + offset) to compress large ranges (e.g., GA4 click counts spanning 1 to 100,000). The offset parameter (default 1) avoids log(0).

"minmax"

Scale to the [0, 1] range using min-max normalisation. A small floor (floor_value, default 0.01) is added so that the lowest-weighted edge still carries some weight rather than zero.

"percentile"

Map values to their empirical percentile (0–1). Robust to extreme outliers.

alpha

Numeric, exponent for the "zipf" method. Default 1.0. Higher values make the drop-off steeper (position 1 dominates more).

offset

Numeric, added to x before the "log" transform. Default 1 (so that zero-valued inputs produce log(1) = 0 rather than -Inf).

floor_value

Numeric, minimum weight for the "minmax" method. Default 0.01.

descending

Logical. For rank-based methods ("rank_linear", "zipf"), whether higher input values get higher weights. Default TRUE (e.g., if the input is click counts, more clicks = higher weight). Set to FALSE when the input is link position on a page (position 1 = most valuable, but numerically smallest).

Value

Numeric vector of the same length as x with transformed weights. NA values in x are preserved as NA in the output.

Examples

# Link positions on a page (1 = top, most valuable)
positions <- c(1, 2, 3, 4, 5)
transform_weights(positions, "rank_linear", descending = FALSE)
#> [1] 1.0 0.8 0.6 0.4 0.2
transform_weights(positions, "zipf", alpha = 1, descending = FALSE)
#> [1] 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000
transform_weights(positions, "zipf", alpha = 2, descending = FALSE)
#> [1] 1.0000000 0.2500000 0.1111111 0.0625000 0.0400000

# GA4 click counts (wide range)
clicks <- c(50000, 12000, 800, 150, 3)
transform_weights(clicks, "log")
#> [1] 10.819798  9.392745  6.685861  5.017280  1.386294
transform_weights(clicks, "minmax")
#> [1] 1.00000000 0.24755485 0.02578155 0.01291077 0.01000000
transform_weights(clicks, "zipf")
#> [1] 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000

# Use with pagerank()
edges <- data.frame(
  from = c("Home", "Home", "Home"),
  to = c("About", "Blog", "Contact"),
  position = c(1, 2, 5)
)
edges$weight <- transform_weights(edges$position, "zipf",
  descending = FALSE
)
# pagerank(edges, weight_col = "weight", clean_edge_urls = FALSE)