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Table 5 Empirical standard deviation of \({{\widehat{p}}}(3)\), and the variation of spectral gap \((\delta )\) and \(\Lambda (3)\) (from the bound of the variance of \({{\widehat{p}}}(3)\)) with N2V-2 (\(w_{ij}=1 , a(i) \ne a(j))\) under model class \(\mathscr {P}(\alpha , \mu , f)\) where \(N=2000\), \(\alpha =0.2\), \(\mu = (0.7, 0.2,0.1)\), \(f(a,a)=0.8\), \(f(a,a')=0.1\), \(a\ne a'=1,2,3\) and \(m=2\)

From: Learning attribute and homophily measures through random walks

\(w_{ij}, a(i) = a(j)\)

0.05

0.25

0.5

0.75

1

1.25

1.5

SD

0.070

0.054

0.058

0.059

0.062

0.073

0.075

Spectral gap \((\delta )\)

0.027

0.098

0.1344

0.139

0.137

0.130

0.122

\(\Lambda (3)\)

0.142

0.115

0.124

0.137

0.149

0.160

0.171