 If the degree distribution of the network follows a power-law, the network is scale-free; if any two arbitrary nodes in a network can be connected in a very small number of steps, the network is said to be small-world.The small-world properties can be mathematically expressed by the slow increase of the average diameter of the network, with the total number of nodes formula_1,

formula_2

where formula_3 is the shortest distance between two nodes.Equivalently, we obtain