dispersion: Dispersion (Backstrom-Kleinberg 2014)

In cograph: Analysis and Visualization of Complex Networks

Dispersion (Backstrom-Kleinberg 2014)

Description

Per-pair measure of tie strength from the Facebook relationship-inference paper. For each pair (u, v) where v is a neighbor of u:

Usage

dispersion(x, u = NULL, v = NULL, normalized = TRUE, alpha = 1, b = 0, c = 0)

Arguments

x	Network input (matrix, igraph, network, cograph_network, tna object).
u	Optional source node (1-based index or node name). If NULL (default), compute for all sources.
v	Optional target node. If NULL, compute for all neighbors of u.
normalized	Logical. If TRUE (default), return the normalized form; otherwise the raw count.
alpha	Numeric normalization exponent. Default 1.
b	Numeric bias added to dispersion before exponentiation. Default 0.
c	Numeric bias added to embeddedness in the denominator. Default 0.

Details

1. Let S_T = N(u) \cap N(v) be their mutual friends (embeddedness).

2. Count pairs (s, t) \subset S_T such that:

   • s and t are not directly connected, AND

   • s and t share no common neighbor inside N(u) other than u and v.

3. The raw dispersion is this count. When normalized = TRUE, the result is (\mathrm{dispersion} + b)^{\alpha} / (\mathrm{embeddedness} + c) (normalization is skipped when embeddedness + c == 0).

Matches networkx.dispersion bit-exact for all three call modes (single pair, single source, full matrix).

Value

• Scalar if both u and v are specified.

• Named numeric vector if exactly one of u, v is given (names are the other endpoints).

• A data frame with columns from, to, dispersion when neither u nor v is given (one row per ordered edge).

References

Backstrom, L., & Kleinberg, J. (2014). Romantic partnerships and the dispersion of social ties: A network analysis of relationship status on Facebook. In Proceedings of CSCW (pp. 831-841). ACM. https://arxiv.org/pdf/1310.6753v1.pdf

Examples

g <- igraph::make_graph("Zachary")
# Node 0 (R index 1) to node 33 (R index 34)
dispersion(g, u = 1, v = 34)
# All pairs from node 1
head(dispersion(g, u = 1))

cograph documentation built on May 31, 2026, 5:06 p.m.