Organization of feed-forward loop motifs reveals architectural principles in natural and engineered networks

Network motifs are significantly overrepresented subgraphs that have been proposed as building blocks for natural and engineered networks. Detailed functional analysis has been performed for many types of motif in isolation, but less is known about how motifs work together to perform complex tasks. To address this issue, we measure the aggregation of network motifs via methods that extract precisely how these structures are connected. Applying this approach to a broad spectrum of networked systems and focusing on the widespread feed-forward loop motif, we uncover striking differences in motif organization. The types of connection are often highly constrained, differ between domains, and clearly capture architectural principles. We show how this information can be used to effectively predict functionally important nodes in the metabolic network of Escherichia coli. Our findings have implications for understanding how networked systems are constructed from motif parts and elucidate constraints that guide their evolution.