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Newton's centuries-old wisdom of standing on the shoulders of giants raises a crucial yet underexplored question: Out of all the prior works cited by a discovery, which one is its giant? Here, we develop a novel, discipline-independent method to identify the giant for any individual paper, allowing us to systematically examine the role and characteristics of giants in science. We find that across disciplines, about 95% of papers stand on the shoulders of giants, yet the weight of scientific progress rests on relatively few shoulders. Defining a new measure of giant index, we find that, while papers with high citations are more likely to be giants, for papers with the same citations, their giant index sharply predicts a paper's future impact and prize-winning probabilities. Giants tend to originate from both small and large teams, being either highly disruptive or highly developmental. And papers that did not have a giant but later became a giant tend to be home-run papers that are highly disruptive to science. Given the crucial importance of citation-based measures in science, the developed concept of giants may offer a useful new dimension in assessing scientific impact that goes beyond sheer citation counts.

We propose a method for extracting hierarchical backbones from a bipartite network. Our method leverages the observation that a hierarchical relationship between two nodes in a bipartite network is often manifested as an asymmetry in the conditional probability of observing the connections to them from the other node set. Our method estimates both the importance and direction of the hierarchical relationship between a pair of nodes, thereby providing a flexible way to identify the essential part of the networks. Using semi-synthetic benchmarks, we show that our method outperforms existing methods at identifying planted hierarchy while offering more flexibility. Application of our method to empirical datasets---a bipartite network of skills and individuals as well as the network between gene products and Gene Ontology (GO) terms---demonstrates the possibility of automatically extracting or augmenting ontology from data., Comment: 8 pages, 4 figures