Network Models of Mechanical Assemblies

Abstract

Recent network research has sought to characterize complex systems with a number of statistical metrics, such as power law exponent (if any), clustering coefficient, community behavior, and degree correlation. Use of such metrics represents a choice of level of abstraction, a balance of generality and detailed accuracy. It has been noted that “social networks” consistently display clustering coefficients that are higher than those of random or generalized random networks, that they have small world properties such as short path lengths, and that they have positive degree correlations (assortative mixing). “Technological” or “non-social” networks display many of these characteristics except that they generally have negative degree correlations (disassortative mixing). [Newman 2003i] In this paper we examine network models of mechanical assemblies. Such systems are well understood functionally. We show that there is a cap on their average nodal degree and that they have negative degree correlations (disassortative mixing). We identify specific constraints arising from first principles, their structural patterns, and engineering practice that suggest why they have these properties. In addition, we note that their main “motif” is closed loops (as it is for electric and electronic circuits), a pattern that conventional network analysis does not detect but which is used by software intended to aid in the design of such systems.