Many social, technological or biological systems are formed by a complex pattern of connections between their constituents; for example, billions of users interact through online networks such as Facebook and Instagram, billions of electronic machines interact via physical connections in the Internet, and thousands of billions of synaptic connections comprise the neural network of our brain. The network structure of such systems is known to have a huge impact on how they operate. Here, I review some of our recent findings about the effect of structure on networked behavior. I present results regarding different aspects of structural properties, including, network hidden geometry, multilayer networks, community structures, and noisy (imperfect) data on structure and/or dynamics. I discuss how each of these properties play a crucial role in various applications such as determining robustness of networks, optimal vaccination strategies, efficient navigation, and identification of the most influential spreaders.
Supported by Science Foundation Ireland funding, MACSI - the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie), centred at the University of Limerick, is dedicated to the mathematical modelling and solution of problems which arise in science, engineering and industry in Ireland.