The cold-start problem is a condition for a new node to join a network with no available information or an isolated node. Most studies use topological network information with the Triadic Closure principles to predict links in future networks. However, the method based on the Triadic Closure principles cannot predict the future link due to no common neighbors between the predicted node pairs. Adamic Adar is one of the methods based on the Triadic Closure principles. This paper proposes three methods for extending Adamic Adar based on network metrics. The main objective is to utilize the network metrics to attract the isolated node or new node to make new relationships in the future network. The proposed method is called the extended Adamic Adar index based on Degree Centrality (DCAA), Closeness Centrality (CloCAA), and Clustering Coefficient (CluCAA). Experiments were conducted by sampling 10% of the dataset as testing data. The proposed method is examined using the four real-world networks by comparing the AUC score. Finally, the experiment results show that the DCAA and CloCAA can predict up to 99% of node pairs with a cold-start problem. DCAA and CloCAA outperform the benchmark, with an AUC score of up to 0,960. This finding shows that the extended Adamic Adar index can overcome prediction failures on node pairs with cold-start problems. In addition, prediction performance is also improved compared to the original Adamic Adar. The experiment results are promising for future research due to successfully improving the prediction performance and overcoming the cold-start problem.