Degree is the simplest of the node-level measures, but its simplicity often hides its power. Here we will apply degree to the problem of mental structure. Specifically, what is the structure of the relationships between information in the mind? George Kingsley Zipf observed that word frequencies in natural language tend to a follow a scale-free distribution: The most frequent words are few, while the less frequent words are many with a specific linear relationship on a log-log plot. It has also been suggested that this power-law distribution applies to the relationships between words as well as to their meanings. Some words share meanings with many other words while others share few. This is a hypothesis based on the structural distribution of shared meanings, or polysemy (words with multiple meanings). This chapter will explain the theory underlying Zipf’s law of meaning and power laws. It will also show how we can combine these ideas with the most basic node-level network measure: degree.

There are two contrasting views of aging. One sees age as a process of cognitive decline, a natural consequence of biological aging. The other sees aging as a process of lifelong learning: Older adults show conspicuous improvements in vocabulary across the lifespan as well as in many other knowledge-related domains. Of these two views, one is based on an underlying process of decay. The other is based on enrichment. Here we will investigate how understanding the nature of structural changes across the lifespan can help align these views, demonstrating how age related cognitive decline can be explained as a process of network enrichment caused by lifelong learning.