Degree Correlations and Motifs in Technological Networks

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. A larger goal of such research is to obtain insight into the systems’ functions by means of these and similar analyses. In this paper we examine network models of mechanical assemblies. Such systems are well understood functionally. We show that they have both rich and varied community structure as well as negative degree correlations (disassortative mixing), and show that this can be explained by additional powerful constraints that arise from identifiable first principles. 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 designed to aid in the design of such systems. The implication is that functional understanding of complex systems requires considerable domain knowledge beyond what typical network analysis tools employ.