Table 1 Logarithmic regressions for the average shortest distance in modular networks.

From: Griffiths phases in infinite-dimensional, non-hierarchical modular networks

 

Vertex networks

Module networks

MMN

〈l〉 = 2.35 + 3.19ln(M)

〈l〉 = −0.22 + 0.71ln(M)

ϕ = 4.0

〈l〉 = 3.67 + 2.88ln(M)

〈l〉 = 0.37 + 0.61ln(M)

ϕ = 2.5

〈l〉 = 7.91 + 1.35ln(M)

〈l〉 = 1.73 + 0.272ln(M)

  1. We analyzed both the original vertex network and the one where modules are considered as vertices connected only by the intermodular edges. Correlation coefficient of the regressions is r2 > 0.999 for MMN and ϕ = 4.0, while r2 = 0.99 for ϕ = 2.5.
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