Geometric Assortative Growth Model for Small-World Networks

Table 1

Properties of model 𝐺(𝑚,𝑡).

	𝑚=1^a	𝑚≥2
Cumulative degree distribution 𝑃cum(𝛿)	(2𝑚)^−𝛿/2𝑚 for large 𝑡
Average neighbor degree 𝑘𝑛𝑛(𝛿)	𝑚^2𝛿2(2𝑚−1) for large 𝑡
Pearson correlation coefficient 𝑟(𝑡)	Increase with 𝑚 as 2(2𝑚)^2+2−(9/(2𝑚−1))3(2𝑚)^2+1−(9/(2𝑚−1)) for large 𝑡
Clustering coefficient 𝑐(𝑡)	Decrease with 𝑚 as (2𝑚−1)(2𝑚)^1/𝑚2𝑚^2ln(2𝑚) for large 𝑡
Transitivity coefficient 𝑐^′(𝑡)	Decrease with 𝑚 as 3𝑚^22(2𝑚−1)(2𝑚)^2+1 for large 𝑡
Diameter diam(𝑡)	𝑡	𝑡+1

a: the properties for 𝐺(1,𝑡) were obtained in [14].