DOI link for Metric-Extremal Graphs
Metric-Extremal Graphs book
A graph is a mathematical object defined as an ordered pair (V ,E) of sets V and E, where V is a (finite or infinite) set of some unspecified elements, called vertices, and E is a set of some (ordered or unordered) pairs of elements of V , called edges. Thus, a graph is an abstract set-theoretical concept. As such, it cannot be viewed as something quantitative.∗ Yet, for most applications of graphs, pertinent numerical indicators are needed, which requires that their structural aspects be quantified (see, for instance, [5,11,16,29,30,33,37,81,91,93,122]). This can be done in many different ways, depending on the nature of the intended application, or on the mathematical apparatus preferred.