Table 9 Given two nodes i and j, there are different metrics that can be used to measure the strength of ties

Adamic-Adar coefficient

\(\sum _{k \in N(i) \cap N(j)} \frac {1}{log N(k)}\), where N(i) refers to the neighbors of a node i.

[19, 33]

Clustering coefficient

\(\frac {2 e_{i}}{(k_{i} (k_{i} -1))}\), where e _i is the number of edges between all neighbors

[4, 33]

of i and k _i is the number of neighbors of i.

Collaboration weight

\(\sum _{p} \frac {\delta _{i}^{p} \delta _{j}^{p}}{n_{p} - 1}\), where \(\delta _{i}^{p}\) is 1 if node i collaborates in a work p and 0

[25, 27]

otherwise, n _p is the number of collaborators in a work p, and all

single-collaborated work are excluded.

Frequency or interaction intensity

w _i,j represents the absolute number of interaction between i and j.

[26]

Neighborhood overlap or Jaccard

\( \frac {|X_{c_{i}} \ \cap \ X_{c_{j}}|}{(|X_{c_{i}} \ \cup \ X_{c_{j}}| \ - \ (i,j \ \text {themselves}))}\), where \(X_{c_{i}}\) represents the neighbors of

[4, 13, 24, 26, 27]

Index or Topological Overlap

node i, and \(X_{c_{2}}\) the neighbors of j.

Normalized direct social weight

\(\frac {\sum _{\forall \lambda \in \Lambda _{i,j}} \omega (i,j,\lambda)}{\sum _{\forall k \in N{i}} \sum _{\forall \lambda \in \Lambda _{i,k}} \omega (i,k,\lambda)}\), where λ∈Λ represents all types of

[34]

interactions (e.g., number of co-authored papers or shared projects)

between i and j.