The 'Middle' of a Graph: Partitions, Eccentricities and Degress of Vertices in a Graph

Diagrams consisting of dots and lines (see Figure 1) called graphs are a very powerful visual tool for helping understand many topics within mathematics and applications of mathematics to other fields. In particular one can find the distance between the objects one represents using the dots in the graphs. This enables one to find vertices in the "middle" of graph in much the same way that a mean or median allows one to pick out a "middle" number for a collection of numbers. A middle vertex might be a good choice for locating a vaccination center.