Graph Theory and Network Science: The Basics Graph theory and
network science are two related academic fields that have found
application in numerous commercial industries. The terms ‘graph’
and ‘network’ are synonymous and one or the other is favored
depending on the domain of application. A Rosetta Stone of
terminology is provided below to help ground the academic terms
to familiar, real-world structures. Graph theory is a branch of
discrete mathematics concerned with proving theorems and
developing algorithms for arbitrary graphs (e.g. random graphs,
lattices, hierarchies). For example, can a graph with four
vertices, seven edges, and structured according to the
landmasses and bridges of Königsberg have its edges traversed
once and only once? From such problems, the field of graph
theory has developed numerous algorithms that can be applied to
any graphical structure irrespective of the domain it represents
(i.e. irrespective of what the graph models in the real-world).
Examples of such developments are pr