Physica A 469 (2017) 767–776 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Link direction for link prediction Ke-ke Shang a,b,∗ , Michael Small b,c , Wei-sheng Yan a a School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, PR China b School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia, 6009, Australia c Mineral Resources, CSIRO, Kensington, Western Australia, 6151, Australia highlights • Various directional links play different prediction roles by mathematical analysis. • Bi-directional links are more informative for link prediction by real data testing. • We propose a new directional randomized algorithm to analysis the role of direction. article info Article history: Received 13 May 2016 Received in revised form 16 November 2016 Available online 24 November 2016 Keywords: Link prediction Directed network Bi-directional links One-directional links Phase dynamics algorithm Directional randomized algorithm abstract Almost all previous studies on link prediction have focused on using the properties of the network to predict the existence of links between pairs of nodes. Unfortunately, previous methods rarely consider the role of link direction for link prediction. In fact, many real- world complex networks are directed and ignoring the link direction will mean overlooking important information. In this study, we propose a phase-dynamic algorithm of the directed network nodes to analyse the role of link directions and demonstrate that the bi-directional links and the one-directional links have different roles in link prediction and network structure formation. From this, we propose new directional prediction methods and use six real networks to test our algorithms. In real networks, we find that compared to a pair of nodes which are connected by a one-directional link, a pair of nodes which are connected by a bi-directional link always have higher probabilities to connect to the common neighbours with only bi-directional links (or conversely by one-directional links). We suggest that, in the real networks, the bi-directional links will generally be more informative for link prediction and network structure formation. In addition, we propose a new directional randomized algorithm to demonstrate that the direction of the links plays a significant role in link prediction and network structure formation. © 2016 Elsevier B.V. All rights reserved. 1. Introduction Link prediction is the key problem of predicting the location of unknown links from uncertain structural information for a network. In biological fields, researchers allocate significant expense to recovering these unknown interactions [1, 2]. Fortunately, link prediction algorithms can help us identify unknown potential interactions to reduce the cost of ∗ Corresponding author at: School of Mathematics and Statistics, The University of Western Australia, Crawley, Western Australia, 6009, Australia. E-mail address: keke.shang@uwa.edu.au (K.-k. Shang). http://dx.doi.org/10.1016/j.physa.2016.11.129 0378-4371/© 2016 Elsevier B.V. All rights reserved.