Table 2 Table of notation for a conventional network G in algorithms

G.n

Set of nodes in network G

G.e

Set of edges in network G

\(d_G\)

Degree frequency list for network G

\(d_G({\mathbf{i}})\)

Degree of node i in network G

\(G.N({\mathbf{i}})\)

Set of neighbors of node i in Network G

\(dist(G,{\mathbf{u}},{\mathbf{v}})\)

Distance between two nodes u and v in Network G

M.col/M.row

Column/row size of a matrix M

M(i,  : )/M( : , i)

ith row/column of matrix M

V(i)

ith element of vector V

V.index(a)

Index of element a in vector V

|S|

Size (the number of elements) of a set S

S.remove(m)

Remove member m from a set S

S.sample(P)

Randomly select an element with property P (if P = 1 there is no property) from set S

urn

Uniform random number in [0, 1]