  For a non-empty ground set $X$, finite or infinite, the {\em set-valuation}
or {\em set-labeling} of a given graph $G$ is an injective function $f:V(G) \to
\mathcal{P}(X)$, where $\mathcal{P}(X)$ is the power set of the set $X$. A
set-indexer of a graph $G$ is an injective set-valued function $f:V(G) \to
\mathcal{P}(X)$ such that the function $f^{\ast}:E(G)\to
\mathcal{P}(X)-\{\emptyset\}$ defined by $f^{\ast}(uv) = f(u){\ast} f(v)$ for
every $uv{\in} E(G)$ is also injective., where $\ast$ is a binary operation on
sets. An integer additive set-indexer is defined as an injective function
$f:V(G)\to \mathcal{P}({\mathbb{N}_0})$ such that the induced function
$g_f:E(G) \to \mathcal{P}(\mathbb{N}_0)$ defined by $g_f (uv) = f(u)+ f(v)$ is
also injective, where $\mathbb{N}_0$ is the set of all non-negative integers
and $\mathcal{P}(\mathbb{N}_0)$ is its power set. An IASI $f$ is said to be a
strong IASI if $|f^+(uv)|=|f(u)|\,|f(v)|$ for every pair of adjacent vertices
$u,v$ in $G$. In this paper, we critically and creatively review the concepts
and properties of strong integer additive set-valued graphs.
