  We propose a definition of {\it security} and a definition of {\it
robustness} of networks against the cascading failure models of deliberate
attacks and random errors respectively, and investigate the principles of the
security and robustness of networks. We propose a {\it security model} such
that networks constructed by the model are provably secure against any attacks
of small sizes under the cascading failure models, and simultaneously follow a
power law, and have the small world property with a navigating algorithm of
time complex $O(\log n)$. It is shown that for any network $G$ constructed from
the security model, $G$ satisfies some remarkable topological properties,
including: (i) the {\it small community phenomenon}, that is, $G$ is rich in
communities of the form $X$ of size poly logarithmic in $\log n$ with
conductance bounded by $O(\frac{1}{|X|^{\beta}})$ for some constant $\beta$,
(ii) small diameter property, with diameter $O(\log n)$ allowing a navigation
by a $O(\log n)$ time algorithm to find a path for arbitrarily given two nodes,
and (iii) power law distribution, and satisfies some probabilistic and
combinatorial principles, including the {\it degree priority theorem}, and {\it
infection-inclusion theorem}. By using these principles, we show that a network
$G$ constructed from the security model is secure for any attacks of small
scales under both the uniform threshold and random threshold cascading failure
models. Our security theorems show that networks constructed from the security
model are provably secure against any attacks of small sizes, for which natural
selections of {\it homophyly, randomness} and {\it preferential attachment} are
the underlying mechanisms.
