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

From: The strength of co-authorship ties through different topological properties

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. [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 λΛ represents all types of [34]
  interactions (e.g., number of co-authored papers or shared projects)  
  between i and j.