title: Scale-free models for the structure of business firm networks.
abstract: 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 lambda increases, and disappear for lambda>or=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.
authors.affiliation: Center for Polymer Studies, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Maksim
authors.initials: M
authors.lastname: Kitsak
authors.forename: Massimo
authors.initials: M
authors.lastname: Riccaboni
authors.forename: Shlomo
authors.initials: S
authors.lastname: Havlin
authors.forename: Fabio
authors.initials: F
authors.lastname: Pammolli
authors.forename: H Eugene
authors.initials: HE
authors.lastname: Stanley
mesh_terms: D000465:Algorithms; D020811:Biomedical Technology; D003146:Communications Media; D007255:Information Services; D018803:Models, Economic; D013997:Time Factors