ABSTRACT
Network models are one of the most popular and powerful tools for probing possible organizational principles in different areas of science. From their origin in graph theory and condensed-matter physics, they have spread across the life and social sciences. During this process of “template transfer,” models developed in one scientific context become adapted to new domains of application, while still retaining many of their original characteristics and limitations. One of these limitations is an excessive focus on static structure rather than dynamics. Even when network dynamics are considered, the focus mainly lies on linear analysis around steady states, and the structure of a model is usually treated as time-invariant. This severely limits the applicability of the network approach to systems whose properties depend on transient behavior and self-organizing, time-variant structures. Such processes are ubiquitous in important classes of complex systems, such as living organisms, ecosystems, neural and cognitive systems, social networks, and the economy. In other words, the space of possibilities of these natural and social systems is much more complex and has a higher dimensionality than the models we use to study them. Here, we examine several case studies to illustrate particular idealizations and limitations and their consequences. This helps us understand why such idealized approaches are successful initially and suggests ways to go beyond the inevitable constraints that arise after model template transfer to a new area of investigation.
