On Motifs and Functional Blocks in Technological Networks

One primary focus of complex systems research has been the topological analysis of the network underlying a complex system. One key question is the size and structure/function of the underlying building blocks. Two proposed building blocks are called motif and functional module. A motif has been defined as a subgraph that occurs significantly more frequently in real-world networks than expected by chance alone [5]. The observed over-representation of motifs has been interpreted as a manifestation of functional constraints and design principles that have shaped network architectures at the local level. In contrast, a functional module or block in a network is a set of nodes that have strong interactions and a distinct function [1]. We distinguish the two by emphasizing small size and recurrence for motifs, endowing modules with larger size, and perhaps a composition dominated by interconnected motifs [7]. However, the relation between motifs and functional blocks lacks adequate precision, and has not received sufficient experimental analysis. This article addresses the relation between motifs and functional modules (or blocks) for a class of complex network, electronic circuits, where nodes are electronic components (e.g. logic gates and flip-flops in digital circuits), and edges are wires [2]. We compared a library of functional modules used by engineers for circuit design with the modules that are automatically identified using motif-finding algorithms [6]. This library of circuit functional blocks was either reverseengineered [3] or identified from IC databooks, cell libraries or textbooks. Given this library, we calculated the relative frequency of the occurrence of the functional modules; we also compared the topologies and instances of motifs and functional blocks. Comparing the hand-generated functional modules with the experimentally-computed motifs showed that: (1) functional modules are much larger than the 3-4 node motifs proposed in [4], and (2) a functional module typically consists of a collection of several 3-4 node motifs. We argue that, for electronic circuits, the statistical overrepresentation of 3-4 node motifs is due to functional modules consisting of motif-clusters, and not that motifs, in and of themselves, play a significant functional role in a circuit. More generally, the common functional modules discovered in benchmark circuits can be considered as “large motifs” themselves.