TABLE 1.

Network properties for typical network types.

Network types	Network properties
	Degree distribution	Average path length	Cluster coefficient
All-to-all network (Albert and Barabasi, 2002; Newman, 2003)	k = N−1	L = 1	C = 1
Regular network (Albert and Barabasi, 2002; Newman, 2003)	k = K	$L\approx \frac{N}{2K}$	$C=\frac{3(K-2)}{4(K-1)}$
Random network (Bollobás, 2001)	$P(k)=C_N^k{p}^k{(1-p)}^{N-k}$	$L\propto \frac{\ln N}{\ln p(N-1)}$	C = p
NW Small-world network (Newman, 2002)	$\begin{array}{c}P(k)=C_N^{k-K}{\left(\frac{Kp}{N}\right)}^k{\left(1-\frac{Kp}{N}\right)}^{N-k+K}\hfill \\ k\ge K\hfill \end{array}$	$L=\frac{N}{2db}F(pb{N}^d),N=\xi$	$C=\frac{3(K-2)}{4(K-1)+4Kp(p+2)}$
Scale-free network (Dorogovtsev et al., 2000; Cohen and Havlin, 2003; Fronczak et al., 2003)	$P(k)=\frac{2m(m+1)}{k(k+1)(k+2)}$	$L\propto \frac{\log N}{\log \log N}$	$C=\frac{m^2{(m+1)}^2}{4(m-1)}[\ln (\frac{m+1}{m})-\frac{1}{m+1}]\frac{{[\ln t]}^2}{t}$

N is the number of nodes, k is the degree of the node, K is the degree of the node in random network and is a fixed value in NW small-world network, p is the probability of two nodes connected, ξ is Characteristic length unit, b is the number of network edges, d is degree of separation, and $\xi =\{\begin{array}{c}\frac{1}{pd},d=1\hfill \\ \frac{1}{pb{d}^{\frac{1}{d}}},d>2\hfill \end{array}$, F is an universal computing function and $F(x)=\{\begin{array}{c}\frac{1}{4},x<1\hfill \\ \frac{\log 2x}{4x},x\ge 1\hfill \end{array}$, m is the number of existing nodes and t is the step size in building a scale-free network.