Table 1 Parameters set to fit a model to a given graph, and to produce a scaled-up replica
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)) u∈V | \(d = \cup _{i=1}^{x} (\deg (u))_{u \in V}\) |
Edge-Switching Markov Chain | E M C(d) | d=(deg(u)) u∈V | \(d = \cup _{i=1}^{x} (\deg (u))_{u \in V}\) |
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)) u∈V )} | n=x·n \(\bar {d} = 2 \cdot (m / n)\) γ= max{2.1,plfit((deg(u)) u∈V )} |
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)) u∈V ) ζ s ={|C| | C∈PLM(O)} β,c min,c max=plfit*(ζ s ) | n ′=x·n γ,d min,d max=plfit((deg(u)) u∈V ) ζ s ={|C| | C∈PLM(O)} β,c min,c max=plfit*(ζ s ) |