Since its introduction in the year 1998 by Watts and Strogatz, the clustering coefficient has become a frequently used tool for analyzing graphs. In 2002 the transitivity was proposed by Newman, Watts and Strogatz as an alternative to the clustering coefficient. As many networks considered in complex systems are huge, the efficient computation of such network parameters is crucial. Several algorithms with polynomial running time can be derived from results known in graph theory. The main contribution of this work is a new fast approximation algorithm for the weighted clustering coefficient which also gives very efficient approximation algorithms for the clustering coefficient and the transitivity. We namely present an algorithm with running time in O(1) for the clustering coefficient, respectively with running time in O(n) for the transitivity. By an experimental study we demonstrate the performance of the proposed algorithms on real-world data as well as on generated graphs. Moreover we give a simple graph generator algorithm that works according to the preferential attachment rule but also generates graphs with adjustable clustering coefficient.
The dynamic analysis of structural change in the organization of the sciences requires, methodologically, the integration of multivariate and time-series analysis. Structural change-for instance, interdisciplinary development-is often an objective of government interventions. Recent developments in multidimensional scaling (MDS) enable us to distinguish the stress originating in each time-slice from the stress originating from the sequencing of time-slices, and thus to locally optimize the trade-offs between these two sources of variance in the animation. Furthermore, visualization programs like Pajek and Visone allow us to show not only the positions of the nodes, but also their relational attributes such as betweenness centrality. Betweenness centrality in the vector space can be considered as an indicator of interdisciplinarity. Using this indicator, the dynamics of the citation-impact environments of the journals Cognitive Science, Social Networks, and Nanotechnology are animated and assessed in terms of interdisciplinarity among the disciplines involved.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.