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www.caida.org > publications : papers : 2010 : scalefreestructurebusiness
Scale-free models for the structure of business firm networks
M. Kitsak, M. Riccaboni, S. Havlin, F. Pammolli, and H. Stanley, "Scale-free models for the structure of business firm networks", Physical Review E, vol. 81, Mar 2010.
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Scale-free models for the structure of business firm networks

Maksim Kitsak1, 2
Massimo Riccaboni2, 3
Shlomo Havlin2, 4, 6
Fabio Pammolli2, 5
H. Eugene Stanley2
1

CAIDA, San Diego Supercomputer Center, University of California San Diego

2

Center for Polymer Studies, Boston University

3

DISA University of Trento

4

Department of Physics, Bar-Ilan University

5

IMT Institute for Advanced Studies

6

Minerva Center

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.

Keywords: network geometry, topology
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