tmep

classes), and edges represent synaptic connections between the neurons. We found the feedforward loop motif in agreement with anatomical observations of triangular connectivity structures (24). The four-node motifs include the bi-fan and the bi-parallel (Table 1). Two of these motifs (feedforward loop and bi-fan) were also found in the transcriptional gene regulation networks. This similarity in motifs may point to a fundamental similarity in the design constraints of the two types of networks. Both networks function to carry information from sensory components (sensory neurons/transcription factors regulated by biochemical signals) to effectors (motor neurons/structural genes). The feedforward loop motif common to both types of networks may play a functional role in information processing. One possible function of this circuit is to activate output only if the input signal is persistent and to allow a rapid deactivation when the input goes off (11). Indeed, many of the input nodes in the neural feedforward loops are sensory neurons, which may require this type of information processing to reject transient input fluctuations that are inherent in a variable or noisy environment. We also studied several technological networks. We analyzed the ISCAS89 benchmark set of sequential logic electronic circuits (7, 25). The nodes in these circuits represent logic gates and flip-flops. These nodes are linked by directed edges. We found that the motifs separate the circuits into classes that correspond to the circuit's functional description. In Table 1, we present two classes, consisting of five forwardlogic chips and three digital fractional multipliers. The digital fractional multipliers share three motifs, including three- and four-node feedback loops. The forward logic chips share the feedforward loop, bi-fan, and bi-parallel motifs, which are similar to the motifs found in the genetic and neuronal information-processing networks. We found a different set of motifs in a network of directed hyperlinks between World Wide Web pages within a single domain (4). The World Wide Web motifs may reflect a design aimed at short paths between related pages. Application of our approach to nondirected networks shows distinct sets of motifs in networks of protein interactions and Internet router connections (18). None of the network motifs shared by the food webs matched the motifs found in the gene regulation networks or the World Wide Web. Only one of the food web consensus motifs also appeared in the neuronal network. Different motif sets were found in electronic circuits with different functions. This suggests that motifs can define broad classes of networks, each with specific types of elementary structures. The motifs reflect the underlying processes that generated each type of network; for example, food webs evolve to allow a flow of energy from the bottom to the top of food chains, whereas gene regulation and neuron networks evolve to process information. Information processing seems to give rise to significantly different structures than does energy flow. We further characterized the statistical significance of the motifs as a function of network size, by considering pieces of various sizes (subnetworks) of the full network. The concentration of motifs in the subnetworks is about the same as that in the full network (Fig. 3). In contrast, the concentration of the corresponding subgraphs in the randomized versions of the subnetworks decreases sharply with size. In analogy with statistical physics, the number of appearances of each motif in the real networks