Table 3 Baseline link prediction methods for temporal networks.

Common neighbors (CN)

The algorithm uses the number of common neighbors as an indicator to measure the possibility of establishing a link between two nodes¹³

\(CN\_ASF(x,y)=\frac{1}{2}\sum \limits _{z \in \Gamma (x) \cap \Gamma (y)}A^T_{x,z}+A^T_{y,z}\)

Jaccard Index (JA)

This algorithm evaluates the probability of connecting edges also by measuring the number of common neighbors, it is the normalized version of \(CN\_ASF\)¹⁶

\(JA\_ASF(x,y)=CN\_ASF(x,y)/(w^T(x)+w^T(y))\)

Preferential Attachment (PA)

In this algorithm, the probability that the target link is connected is proportional to the product of the degrees of the two endpoints, it is a hub-promoted method⁵³

\(PA\_ASF(x,y)=w^T(x) \cdot w^T(y)\)

Resource Allocation (RA)

Common neighbors serve as a medium for resource transfer, and the weight of common neighbors is inversely proportional to its degree¹⁷

\(RA\_ASF(x,y)=\sum \limits _{z \in \Gamma (x) \cap \Gamma (y)}\frac{1}{w^T(z)}\)

Cannistrai Alanis Ravai (CAR)

The algorithm utilizes the links between commmon neighbors, along with commmon neighbors information, where LCL’(x,y) is total weights of links between common-neighbors¹⁴

\(CAR\_ASF(x,y)=CN\_ASF(x,y)\cdot LCL'(x,y)\)

Clustering Coefficient-based Index (CCLP)

This metric employs clustering coefficient of common neighbors to reflect the density of triangles within a local network environment, where \(\Delta '\) is the total weight of weighted triangles among common-neighbors¹⁵

\(CCLP\_ASF(x,y)=\sum \limits _{z \in \Gamma (x) \cap \Gamma (y)}\frac{\Delta '}{d(z)\cdot (d(z)-1)/2}\)