  In this paper, a novel graph-theoretic framework is proposed to generalize
the analysis of a broad set of security attacks, including observability and
data injection attacks, that target the state estimator of a smart grid. First,
the notion of observability attacks is defined based on a proposed
graph-theoretic construct. In this respect, a structured approach is proposed
to characterize critical sets, whose removal renders the system unobservable.
It is then shown that, for the system to be observable, these critical sets
must be part of a maximum matching over a proposed bipartite graph. In
addition, it is shown that stealthy data injection attacks (SDIAs) constitute a
special case of these observability attacks. Then, various attack strategies
and defense policies, for observability and data injection attacks, are shown
to be amenable to analysis using the introduced graph-theoretic framework. The
proposed framework is then shown to provide a unified basis for analysis of
four key security problems (among others), pertaining to the characterization
of: 1) The sparsest SDIA; 2) the sparsest SDIA including a certain measurement;
3) a set of measurements which must be defended to thwart all potential SDIAs;
and 4) the set of measurements, which when protected, can thwart any SDIA whose
cardinality is below a certain threshold. A case study using the IEEE 14-bus
system with a set of 17 measurements is used to support the theoretical
findings.
