Table 1.

A summary of common notations

G(V, E)	Undirected network
V	Set of nodes
E	Set of edges
n	Number of nodes
m	Number of edges
$s_{\mathit{xy}}$	Similarity score of node x and node y
$d_m$	Maximum degree of a network
$d_{m}in$	Minimal degree of a network
d(v)	Number of edges connecting to node v
${\mathrm{\Gamma }}_x$	Set of neighbors of node x
l	Number of random walk steps
L	Laplacian matrix
S	Similarity matrix
M	Direct similarity
A	Adjacent matrix
I	Identity matrix
$a,ϵ,\beta ,\varphi ,\psi$	Parameters
P	Transition probability matrix
${\pi }_{\mathit{xy}}$	Probability of a walker starting from x and locating at y