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

Description Equation Publications
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. 
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 λΛ represents all types of 
interactions (e.g., number of co-authored papers or shared projects)
between i and j. 