Table 4.

ROC-AUC scores for link prediction on the 7 reference multiplex networks, for link prediction heuristics (CN-av, AA-av, JC-av, PA-av) and network embedding methods combined with different operators (Hadamard, Weighted-L1, Weighted-L2, Average, and Cosine).

Operators	Method	CKM	LAZEGA	C.ELE	ARXIV	DIS	HOMO	MOL
Link prediction heuristics	CN-av	0.4944	0.6122	0.5548	0.5089	0.5097	0.5113	0.5408
	AA-av	0.4972	0.6105	0.549	0.5081	0.5428	0.5112	0.5404
	JC-av	0.4911	0.523	0.5424	0.5113	0.5425	0.5113	0.5433
	PA-av	0.5474	0.6794	0.5634	0.5139	0.496	0.5185	0.5278
Hadamard	node2vec-av	0.7908	0.6372	0.8552	0.9775	0.9093	0.8638	0.8753
	deepwalk-av	0.7467	0.6301	0.8574	0.9776	0.9107	0.8638	0.8763
	LINE-av	0.5073	0.4986	0.5447	0.8525	0.9013	0.8852	0.8918
	Ohmnet	0.7465	0.7981	0.833	0.9605	0.9333	0.9055	0.8613
	MNE	0.5756	0.6356	0.794	0.9439	0.9099	0.8313	0.8736
	Multi-node2vec	0.8182	0.7884	0.8375	0.9581	0.8528	0.8592	0.8835
	MultiVERSE	0.8177	0.8269	0.8866	0.9937	0.9401	0.917	0.9259
Weighted-L1	node2vec-av	0.7532	0.737	0.8673	0.9738	0.885	0.6984	0.7976
	deepwalk-av	0.7226	0.7094	0.8635	0.9751	0.8888	0.7142	0.8089
	LINE-av	0.6091	0.5776	0.6192	0.7539	0.8586	0.7439	0.7792
	Ohmnet	0.7421	0.7849	0.8128	0.8488	0.8503	0.7007	0.6983
	MNE	0.6289	0.6523	0.8019	0.7805	0.8313	0.7619	0.8182
	Multi-node2vec	0.8611	0.8089	0.8261	0.9659	0.8628	0.8472	0.8997
	MultiVERSE	0.7043	0.7789	0.7516	0.8647	0.7754	0.683	0.7273
Weighted-L2	node2vec-av	0.7556	0.6851	0.8691	0.9743	0.8867	0.7048	0.8028
	deepwalk-av	0.7221	0.6904	0.864	0.9771	0.8891	0.7145	0.813
	LINE-av	0.5851	0.5756	0.6275	0.7609	0.8621	0.7429	0.7835
	Ohmnet	0.7505	0.7788	0.8166	0.8439	0.8599	0.7041	0.6992
	MNE	0.601	0.5397	0.7999	0.7815	0.8333	0.7483	0.8122
	Multi-node2vec	0.8637	0.8091	0.8282	0.968	0.8675	0.8525	0.9004
	MultiVERSE	0.7125	0.7801	0.7441	0.8661	0.7808	0.6918	0.7475
Average	node2vec-av	0.59	0.6596	0.6842	0.6615	0.8256	0.8308	0.777
	deepwalk-av	0.5954	0.657	0.6784	0.6582	0.8267	0.8307	0.7737
	LINE-av	0.5465	0.6581	0.6699	0.6465	0.8477	0.8653	0.8276
	Ohmnet	0.5764	0.656	0.7334	0.6772	0.8533	0.8825	0.7962
	MNE	0.5882	0.6615	0.7028	0.6723	0.8242	0.8024	0.783
	Multi-node2vec	0.5571	0.6584	0.7365	0.6657	0.8222	0.8216	0.7589
	MultiVERSE	0.5963	0.6728	0.7438	0.6752	0.8586	0.8643	0.812
Cosine	node2vec-av	0.7805	0.7335	0.8515	0.9711	0.8643	0.7368	0.8105
	deepwalk-av	0.7465	0.7066	0.8416	0.9724	0.8667	0.7512	0.8079
	LINE-av	0.545	0.5126	0.5477	0.8198	0.7409	0.6745	0.816
	Ohmnet	0.7898	0.7352	0.8094	0.9642	0.859	0.7829	0.7909
	MNE	0.6203	0.6506	0.7877	0.8951	0.8347	0.6474	0.8102
	Multi-node2vec	0.8532	0.7931	0.7815	0.9435	0.7151	0.8477	0.8884
	MultiVERSE	0.8148	0.8171	0.8719	0.9909	0.8775	0.8776	0.9103

For each multiplex network, the best score is in bold; for each operator, the best scores are underlined. Overall, the MultiVERSE algorithm combined with the Hadamard shows the best scores.