Jacob G. Foster

Edge direction and the structure of networks.

Directed networks are ubiquitous and are necessary to represent complex systems with asymmetric interactions—from food webs to the World Wide Web. Despite the importance of edge direction for detecting local and community structure, it has been disregarded in studying a basic type of global diversity in networks: the tendency of nodes with similar numbers of edges to connect. This tendency, called assortativity, affects crucial structural and dynamic properties of real-world networks, such as error tolerance or epidemic spreading. Here we demonstrate that edge direction has profound effects on assortativity. We define a set of four directed assortativity measures and assign statistical significance by comparison to randomized networks. We apply these measures to three network classes—online/social networks, food webs, and word-adjacency networks. Our measures (i) reveal patterns common to each class, (ii) separate networks that have been previously classified together, and (iii) expose limitations of several existing theoretical models. We reject the standard classification of directed networks as purely assortative or disassortative. Many display a class-specific mixture, likely reflecting functional or historical constraints, contingencies, and forces guiding the system’s evolution.

Tradition and Innovation in Scientists’ Research Strategies

What factors affect a scientist’s choice of research problem? Qualitative research in the history and sociology of science suggests that this choice is patterned by an “essential tension” between productive tradition and risky innovation. We examine this tension through Bourdieu’s field theory of science, and we explore it empirically by analyzing millions of biomedical abstracts from MEDLINE. We represent the evolving state of chemical knowledge with networks extracted from these abstracts. We then develop a typology of research strategies on these networks. Scientists can introduce novel chemicals and chemical relationships (innovation) or delve deeper into known ones (tradition). They can consolidate knowledge clusters or bridge them. The aggregate distribution of published strategies remains remarkably stable. High-risk innovation strategies are rare and reflect a growing focus on established knowledge. An innovative publication is more likely to achieve high impact than a conservative one, but the additional reward does not compensate for the risk of failing to publish. By studying prizewinners in biomedicine and chemistry, we show that occasional gambles for extraordinary impact are a compelling explanation for observed levels of risky innovation. Our analysis of the essential tension identifies institutional forces that sustain tradition and suggests policy interventions to foster innovation.

Choosing experiments to accelerate collective discovery

Significance Scientists perform a tiny subset of all possible experiments. What characterizes the experiments they choose? And what are the consequences of those choices for the pace of scientific discovery? We model scientific knowledge as a network and science as a sequence of experiments designed to gradually uncover it. By analyzing millions of biomedical articles published over 30 y, we find that biomedical scientists pursue conservative research strategies exploring the local neighborhood of central, important molecules. Although such strategies probably serve scientific careers, we show that they slow scientific advance, especially in mature fields, where more risk and less redundant experimentation would accelerate discovery of the network. We also consider institutional arrangements that could help science pursue these more efficient strategies. A scientist’s choice of research problem affects his or her personal career trajectory. Scientists’ combined choices affect the direction and efficiency of scientific discovery as a whole. In this paper, we infer preferences that shape problem selection from patterns of published findings and then quantify their efficiency. We represent research problems as links between scientific entities in a knowledge network. We then build a generative model of discovery informed by qualitative research on scientific problem selection. We map salient features from this literature to key network properties: an entity’s importance corresponds to its degree centrality, and a problem’s difficulty corresponds to the network distance it spans. Drawing on millions of papers and patents published over 30 years, we use this model to infer the typical research strategy used to explore chemical relationships in biomedicine. This strategy generates conservative research choices focused on building up knowledge around important molecules. These choices become more conservative over time. The observed strategy is efficient for initial exploration of the network and supports scientific careers that require steady output, but is inefficient for science as a whole. Through supercomputer experiments on a sample of the network, we study thousands of alternatives and identify strategies much more efficient at exploring mature knowledge networks. We find that increased risk-taking and the publication of experimental failures would substantially improve the speed of discovery. We consider institutional shifts in grant making, evaluation, and publication that would help realize these efficiencies.

Weaving the fabric of science: Dynamic network models of science's unfolding structure

Abstract Science is a complex system. Building on Latours actor network theory, we model published science as a dynamic hypergraph and explore how this fabric provides a substrate for future scientific discovery. Using millions of abstracts from MEDLINE, we show that the network distance between biomedical things (i.e., people, methods, diseases, chemicals) is surprisingly small. We then show how science moves from questions answered in one year to problems investigated in the next through a weighted random walk model. Our analysis reveals intriguing modal dispositions in the way biomedical science evolves: methods play a bridging role and things of one type connect through things of another. This has the methodological implication that adding more node types to network models of science and other creative domains will likely lead to a superlinear increase in prediction and understanding.

Clustering drives assortativity and community structure in ensembles of networks

Clustering, assortativity, and communities are key features of complex networks. We probe dependencies between these features and find that ensembles of networks with high clustering display both high assortativity by degree and prominent community structure, while ensembles with high assortativity show much less enhancement of the clustering or community structure. Further, clustering can amplify a small homophilic bias for trait assortativity in network ensembles. This marked asymmetry suggests that transitivity could play a larger role than homophily in determining the structure of many complex networks.