For complex networks one can define the volume as the number of nodes j within a distance r ( i , j ) of node i , averaged over i , and the dimension may be defined as the exponent which determines the scaling behaviour of the volume with distance. For a vector n → → = ( n 1 , … … , n d ) ∈ ∈ Z d , where d is a positive integer, the Euclidean norm ‖ ‖ n → → ‖ ‖ is defined as the Euclidean distance from the origin to n → → , i.e.,