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Table 1 Definitions of several similarity indices between two nodes (Gi,Gj) in a GoG \(\mathcal {G}\)

From: Dual graph convolutional neural network for predicting chemical networks

Similarity index

Definition

Common neighbours

\( \mid \mathcal {N}(G_{i})\cap \mathcal {N}(G_{j})\mid \)

Jaccard’s coefficient

\(\frac {\mid \mathcal {N}(G_{i})\cap \mathcal {N}(G_{j})\mid } {\mid \mathcal {N}(G_{i})\cup \mathcal {N}(G_{j})\mid } \)

Katz

\((I-\beta \boldsymbol {\mathcal {A}})^{-1}-I\)

  1. \(\mathcal {N}(G)\) indicates the neighbor set of node G. I is the identity matrix and \({\mathcal {A}}\) is the adjacency matrix of \(\mathcal {G}\). β is the constant parameter that controls path weights depending on their lengths, and we set β=0.001