When hoping to initiate or sustain students' interest in mathematics teachers should always consider relevance, relevance to students' lives and in the middle and later years of instruction in high school and university, accessibility. A topic such as the mathematics behind networks science, more specifically scale-free graphs, is up-to-date, highly relevant to students' lives, and accessible. This article illustrates how mathematicians and scientists work together collaboratively when applying mathematics and developing new scientific theories, and describes ways of teaching mathematics in a highly meaningful, real-world context with a topic which is widely acknowledged as being important mathematically and scientifically. (Contains 4 figures and 4 footnotes.)