Scharnhorst, Andrea

Dynamic networks? concepts and model from non-linear physics and consequences for the analysis of networked research

Abstract

This paper focuses on the mathematical models used in the analysis of the Web and in particular of research networks and their conceptual background.We are surrounded by networks: railway nets and nets of electricity, food webs, neuronal networks and semantic networks.1 Similarly, social networks (including scholarly research networks) are represented through the Web. The Web reinforces the perception of social systems as consisting of networks. Correspondingly, social network analysis faces a revival in the context of internet studies. Based on graph theory, the main focus is directed towards formal properties of social networks, on their structure at a macro-level at a certain point in time. The question is "how are nodes linked to each other"?.

Beside this traditional research line non-linear physics introduces a new research perspective in network analysis (Watts 1999). In particular, it offers explanations for the dynamics, the growth of networks, and for the mechanisms behind emerging network structures. This raises questions about "how come nodes to be linked"? or "why are nodes linked"?. Turned into the question "why link nodes to each other"? a bridge between substantial and formal analysis can be built.

Recently, methods from statistical physics have been applied to the "scientific community" with its networks of co-authorship and citation (Newman 2000). In this line of research, the Web serves as an additional data source to make such research networks visible. Methods and concepts from theoretical physics, scientometrics or cybermetrics merge and are used to explain some of the network phenomena visible on the Web (Bianconi and Barabási 2000; Jain and Krishna 2000).

In this paper, we will analyze this area in-between different disciplines using bibliometric tools first. We start with a group of papers at the border between physics, sociology and science studies and look for their connectivity in the form of citations. In a second step, we will ask for the concepts related to different formal approaches. What are the dominant research questions" How do these various approaches inform each other? How is knowledge transferred between them? Possible points of anchor between formal analysis and substantially oriented network research will be explored.

Notes and References:

1. For illustrative examples see for instance Peter Erdi at http://www.rmki.kfki.hu/biofiz/cneuro/tutorials/kzoo/kzooall/.

2.Bianconi, G. and A.-L. Barabási (2000). Bose-Einstein condensation in complex networks. Last access: December, 2001. See arXiv:cond-mat/0011224v1

3.Jain, S. and S. Krishna (2000). A model for the emergence of cooperation, interdependence and structure in evolving networks. Last access: December 2001, 2001. See http://xxx.lanl.gov/abs/nlin.AO/0005039.

4. Newman, M. E. J. (2000). Who is the best connected scientist? A Study of Scientific Co-authorship Networks. Last access: October 9, 2001. See http://arxiv.org/abs/cond-mat/0011144v1

5.Watts, D. J. (1999). Small Worlds. The Dynamics of Networks between Order and Randomness. Princeton, New Jersey, Princeton University Press.