Networks are not static

Interaction networks can describe many interesting things – human social systems, like facebook, but also complex engineered systems like the internet, or animal societies. The past century has seen the development of an area of mathematics called graph theory, which can be used to describe the structure of these networks. There are statistics that describe how influential or connected different parts of the network are. More recently, models have been developed to explain the structure of these networks, resolving questions like why, for example, most nodes in a network have very few connections but a few tend to be very well-connected.

A key limitation to this kind of work is the fundamental assumption that a system can be described by a single, unchanging network. This is like assuming your circle of friends is static, or that an animal society never sees immigration or death. It’s clearly unrealistic, but capturing the dynamics of networks is surprisingly difficult. Many of our concepts simply don’t work when the system changes in time. The connectedness of a node may change over time – or a pathway of resource flow that looks strong in a static network may actually not exist during some time periods in a dynamic network. Developing new theory to account for these dynamic changes has been a long-standing challenge. There is much to be learned from dynamic networks, since nearly all phenomena of interest are actually dynamic – how networks come together and are taken apart, how persistent are certain structures, why some nodes -become- more important, and so on. Explanation is inherently a historical process, and history implies time.

We’ve recently published a paper surveying temporal dynamics in networks, but have also been thinking about the topic in an educational context. Many people have been interested in networks that are inspired by biology, but don’t have a strong background in animal societies.

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We’ve therefore written a chapter for a new book, Temporal Networks, that focuses on temporal dynamics in social insect networks. The complex societies of ants and bees are a natural example of a network that changes in time in ways shaped by millions of years of adaptive evolution. Perhaps one can learn something from these systems, and apply some of the same ideas we use to study them in other contexts.

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The book chapter surveys the basic biology of social insect networks, and shows several ways in which these societies can be understood in the context of network dynamics. The chapte also shows how task allocation in insect societies is actually quite variable over time, and has important consequences for the overall performance of a society.

You can buy the book from Spring-Verlag, or read the chapter online for free at my website. Dan Charbonneau is the lead author and Anna Dornhaus also contributed.

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