Extract network backbone using the disparity filter

Applies the disparity filter to a weighted edge list. For each edge, it computes an alpha (p-value) from both endpoints and keeps the edge if it is statistically significant from at least one endpoint.

Usage

backbone(edges, alpha = 0.05)

Arguments

edges: A data frame with at least columns from, to, and weight. Must be an undirected edge list (each pair appears once).
alpha: Numeric. Significance threshold in (0, 1). Default 0.05.

Value

The filtered edge data frame with an added alpha column (the minimum alpha from the two endpoints).

Details

The null model asks: given that node $i$ has total strength $s_i$ distributed uniformly across $k_i$ edges, what is the probability that a single edge weight is as large as $w_{ij}$? The answer is $$\alpha_{ij} = \left(1 - \frac{w_{ij}}{s_i}\right)^{k_i - 1}$$

An edge is retained if $\min(\alpha_{ij}, \alpha_{ji}) < \alpha$. Nodes with only one edge always have $\alpha = 0$ and are always kept.

Examples

edges <- data.frame(
  from   = c("A", "A", "A", "B", "C"),
  to     = c("B", "C", "D", "C", "D"),
  weight = c(10,   1,   1,   8,   1)
)
backbone(edges, alpha = 0.05)
#>   from to weight      alpha
#> 1    A  B     10 0.02777778
#> 2    B  C      8 0.04000000