The Topology of Technology Graphs: Small World Patterns in Electronic Circuits

Recent theoretical studies and extensive data analyses have revealed a common feature displayed by biological, social and technological networks: the presence of small world patterns. Here we analyse this problem by using several graphs obtained from one of the most common technological systems: electronic circuits. It is shown that both analogic and digital circuits exhibit SW behavior. We conjecture that the SW pattern arises from the compact design in which many elements share a small, close physical neighborhood plus the fact that the system must define a single connected component (which requires shortcuts connecting different integrated clusters). The degree distributions displayed are consistent with a conjecture concerning the sharp cutoffs associated to the presence of costly connections [Amaral et al., Proc. Natl. Acad. Sci. USA 97 , 11149 (2000)] thus providing a limit case for the classes of universality of small world patterns from real, artificial networks. The consequences for circuit design are outlined.