| Summary: | From biological networks to social networks, we are surrounded by many complex networks with diverse nature and structure. Given the important role these networks play in our daily life, science and economy, their understanding, mathematical description, prediction, and control have become a major intellectual and scientific challenge of the 21st century. In response, the field of Network Science has emerged, drawing on theories and methods including graph theory,
statistical mechanics, data mining, inferential modeling, and social structure. In this dissertation, we focus on the application of Network Science in two distinct areas: network structure and health. In the first chapter, we explore the properties of physical networks, where the nodes and links are physical objects unable to cross each other. These non-crossing conditions constrain their layout geometry and affect how networks form, evolve and function. We developed a modeling
framework that accounts for the physical reality of nodes and links, allowing us to explore how the non-crossing conditions affect the network geometry. For small link thicknesses, we observed a weakly interacting phase where the layout avoids the link crossings via local link rearrangements, without altering the overall layout geometry. Once the link thickness exceeds a critical threshold, a strongly interacting phase emerges, where multiple geometric quantities scale with link
thickness. We observed a deep universality, finding that the observed scaling properties are independent of the underlying network topology. In the second chapter, we investigate the role that diet plays in the development of Coronary Heart Disease (CHD). We applied an Environment-Wide Association Study (EWAS) approach to Nurses' Health Study data to explore comprehensively and agnostically the effect of 257 nutrients and 117 foods on CHD risk. Our implementation of EWAS successfully
reproduced prior knowledge in diet-CHD associations and helped us detect new associations that were previously only poorly studied in the literature. We showed that EWAS allows us to unveil the bipartite food-nutrients network, highlighting which nutrient in which food drives CHD risk. We showed that there is a distinct clustering in this network where protective nutrients and foods are highly interconnected in one cluster, and harmful nutrients and foods in another. Using this network,
we showed that solely looking at food items, one would underestimate the effect of those nutrients whose consumption is strongly determined by the behavioral aspect and not mainly by their average amount in food.
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