Structure of Business Firm Networks and Scale-Free Models.

We study the structure of business firm networks in the Life Sciences (LS) and the Information and Communication Technology (ICT) sectors. We analyze business firm networks and scale-free models with degree distribution P(q) proportional to (q + c)^-λ using the method of k-shell decomposition. We find that the LS network consists 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 ICT network. Our results suggest that the sizes of the nucleus and the tendrils decrease as λ increases and disappear for λ greater or equal to 3. We compare the k-shell structure of random scale-free model networks with the real world business firm networks. 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 regimes in the evolution of industry networks.