Spectral gap of a graph

The spectral (or eigen) gap of a graph is the absolute difference between the biggest and second biggest eigenvalue of the adjacency matrix. To compare spectral gaps across networks, the fraction can be used.

Usage

spectral_gap(g, method = "frac")

Arguments

g

igraph object

method

A string, either "frac" or "abs"

Value

Numeric value

Details

The spectral gap is bounded between 0 and 1 if method="frac", except for complete graphs where the second largest eigenvalue is negative. The closer the value to one, the bigger the gap. Edge weights are ignored.

Author

David Schoch

Examples

# The fractional spectral gap of a threshold graph is usually close to 1
g <- threshold_graph(50, 0.3)
spectral_gap(g, method = "frac")
#> [1] 0.7305571