Order and Size

A graph's order or n, is how many vertices it has given by V(G). M, the number of edges in the graph E(G) determines a graph's size. Graphs can represent all kinds of networks. Vertices may be organs: heart, kidneys or brain, or chips, valves, or some anatomical or functional combinations of these. Edges represent predicted or defined relationships between the vertices. Edges might be roads, flight paths, wires, blood vessels, nerves, tubes, light-paths, routes of diffusing molecules through the hemolymph, or combinations. The elements of a graph and their connections can represent any groupings of characters we choose. This one generalization makes graphs such powerful tools. To make a graph we abstract everything else away. As with the Xeroxed picture of grandmother, what is remarkable is how much information remains in her connected edges.

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