  We study the structure of business firm networks and scale-free models with
degree distribution $P(q) \propto (q+c)^{-\lambda}$ using the method of
$k$-shell decomposition.We find that the Life Sciences industry network consist
of three components: a ``nucleus,'' which is a small well connected subgraph,
``tendrils,'' which are small subgraphs consisting of small degree nodes
connected exclusively to the nucleus, and a ``bulk body'' which consists of the
majority of nodes. At the same time we do not observe the above structure in
the Information and Communication Technology sector of industry. We also
conduct a systematic study of these three components in random scale-free
networks. Our results suggest that the sizes of the nucleus and the tendrils
decrease as $\lambda$ increases and disappear for $\lambda \geq 3$. We compare
the $k$-shell structure of random scale-free model networks with two real world
business firm networks in the Life Sciences and in the Information and
Communication Technology sectors. Our results suggest that the observed
behavior of the $k$-shell structure in the two industries is consistent with a
recently proposed growth model that assumes the coexistence of both
preferential and random agreements in the evolution of industrial networks.
