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oliviatessa authored Dec 19, 2022
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## Background

Complex networks across many domains (ecological food webs, neural systems, electrical circuits) are made up of statistically significant, subgraphs called network motifs. Network motifs are described by the number of nodes they involve and the nature of the connections in-between the nodes (e.g., directed, or bi-directed). The order of the motif is defined by the number of nodes it involves (i.e. n-order motif involves n+1 nodes). For example, a second-order diverging motif involves 3 nodes:
Complex networks across many domains (ecological food webs, neural systems, electrical circuits) are made up of statistically significant, subgraphs called network motifs. Network motifs are described by the number of nodes they involve and the nature of the connections in-between the nodes (e.g., directed, or bi-directed). The order of the motif is defined by the number of nodes it involves (i.e. n-order motif involves n+1 nodes). In a feed-forward neural network, only directed n-order motifs are possible. Here are some 1<sup>st<sup/>-, 2<sup>nd<sup/>-, and 3<sup>rd<sup/>-order motifs possible in a feed-forward neural network:

<p align="center">
<img src="figs/motifs.jpg" width="75%">
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