%0 Journal Article
%@ 1539-3755
%A Kitsak, Maksim
%A Riccaboni, Massimo
%A Havlin, Shlomo
%A Pammolli, Fabio
%A Stanley, H. Eugene
%D 2010
%F eprints:634
%I American Physical Society
%J Physical Review E
%K PACS number(s): 89.75.Hc
%N 3
%P 036117
%T Scale-free models for the structure of business firm networks
%U http://eprints.imtlucca.it/634/
%V 81
%X We study firm collaborations in the life sciences and the information and communication technology sectors. We propose an approach to characterize industrial leadership using k-shell decomposition, with top-ranking firms in terms of market value in higher k-shell layers. We find that the life sciences industry network consists of three distinct 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. Industrial leaders, i.e., the largest companies in terms of market value, are in the highest k-shells of both networks. The nucleus of the life sciences sector is very stable: once a firm enters the nucleus, it is likely to stay there for a long time. At the same time we do not observe the above three components in the information and communication technology sector. 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 in scale-free networks decrease as the exponent of the power-law degree distribution λ increases, and disappear for λ≥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. We argue that the observed behavior of the k-shell structure in the two industries is consistent with the coexistence of both preferential and random agreements in the evolution of industrial networks.
%Z © 2010 American Physical Society