Link structures are important patterns one looks out for when modeling and analyzing social networks. In this paper, we propose the task of mining interesting Link Formation rules (LF-rules) containing link structures known as Link Formation patterns (LF-patterns). LF-patterns capture various dyadic and/or triadic structures among groups of nodes, while LF-rules capture the formation of a new link from a focal node to another node as a postcondition of existing connections between the two nodes. We devise a novel LF-rule mining algorithm, known as LFR-Miner, based on frequent subgraph mining for our task. In addition to using a support-confidence framework for measuring the frequency and signi¯cance of LF-rules, we introduce the notion of expected support to account for the extent to which LF- rules exist in a social network by chance. Specifically, only LF-rules with higher-than-expected support are considered interesting. We conduct empirical studies on two real-world social networks, namely Epinions and myGamma. We report interesting LF-rules mined from the two networks, and compare our findings with earlier findings in social network analysis.