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Table 1 Parameters set to fit a model to a given graph, and to produce a scaled-up replica

From: Generating realistic scaled complex networks

Model Parameters Fitting Fitting scaling by \(x \in \mathbb {N}\)
Erdős–Rényi E R(n ,p) n =n \(p = \frac {2m}{n \cdot (n-1)}\) n =x·n \(p = \frac {2m}{x \cdot n \cdot (n-1)}\)
Barabasi-Albert B A(n ,k) n =n k=m/n n =x·n k=m/n
Chung-Lu C L(d) d=(deg(u)) uV \(d = \cup _{i=1}^{x} (\deg (u))_{u \in V}\)
Edge-Switching Markov Chain E M C(d) d=(deg(u)) uV \(d = \cup _{i=1}^{x} (\deg (u))_{u \in V}\)
R-MAT R M(s,e,(a,b,c,d)) s=log2n e=m/n (a,b,c,d)=kronfit(O) s=log2x·n e=m/n (a,b,c,d)=kronfit(O)
Hyperbolic Unit-Disk \(HUD(n, \bar {d}, \gamma)\) n=n \(\bar {d} = 2 \cdot (m / n)\) γ= max{2.1,plfit((deg(u)) uV )} n=x·n \(\bar {d} = 2 \cdot (m / n)\) γ= max{2.1,plfit((deg(u)) uV )}
BTER B T E R(d,c) \(d = (n_{d})_{d \in (0, \dots, d_{\max })}\) \(c = (c_{d})_{d \in (0, \dots, d_{\max })} \) \(d = (n_{d} \cdot x)_{d \in (0, \dots, d_{\max })}\) \(c = (c_{d})_{d \in (0, \dots, d_{\max })} \)
LFR \(LFR(n',{\newline } \gamma,\bar {d},d_{\max }, {\newline } \beta, c_{\min },c_{\max })\) n =n γ,d min,d max=plfit((deg(u)) uV ) ζ s ={|C| | CPLM(O)} β,c min,c max=plfit*(ζ s ) n =x·n γ,d min,d max=plfit((deg(u)) uV ) ζ s ={|C| | CPLM(O)} β,c min,c max=plfit*(ζ s )