Grid Architecture is largely concerned with structures since we view the power grid as being
comprised of a network of structures: electrical infrastructure, industry structure control structure,
digital superstructure including communications networks, and convergent structures such
as those for water, gas, and transport. These structures are interconnected in complex ways,
and many of the characteristics of the grid that we wish to enhance or add derive directly from
structure or are strongly influenced by it. Consequently it is important to have rigorous methods
to analyze such structures and systematically modify them. These structures are far too complex
to handled by inspection and hence the focus here on applying graph theory to grid structure
problems.
Graphs are abstract structures that express pairwise relationships between entities. Because of
their versatility and universality, graphs are a natural data structure for representing a myriad
of complex systems. The burgeoning field of network science, for which graph theory serves
as a mathematical scaffold, attests to the ubiquity and utility of graph theoretic analyses in farranging
disciplines, including biology, chemistry, social science, and engineering [2]. In the
case of power systems, the application of graph theoretic methods is far from new; see [12] for
a survey of scientific literature on graph theoretic methods applied to the electric grid. Rather
than provide a comprehensive survey here, we aim to provide a self-contained introduction to
selected graph theoretic topics that may have increased pertinence in the structural analysis of
power systems. In particular, we focus on methodologies for defining, scoring, and identifying
connectivity, centrality, and bottleneckeness properties in graphs. We apply these measures
to power systems graph data when possible, frequently present visualizations, and discuss the
computational feasibility of these methods.