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Network Motifs

This overview explores network motifs, distinct patterns that recur more frequently in real networks than in random configurations. It discusses their applications across various domains, including gene networks, neural networks, ecological models, and computer networking. The analysis employs exhaustive methods to identify motifs, examining neural and gene networks that exhibit similarities in structure and function. Notably, motifs reflect underlying interactions and can reveal functional classifications in electronic circuits and links within web pages. The findings suggest motifs may indicate common functions or similar evolutionary pressures in diverse networks.

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Network Motifs

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  1. Network Motifs Zach Saul CS 289 Network Motifs: Simple Building Blocks of Complex Networks R. Milo et al.

  2. Network Models • Interactions are represented as directed nodes (as presented in class) • Example problems include gene networks, neural nets, ecological models and computer networking models

  3. Network Motifs • Patterns that appear more often in real networks than in randomly generated networks • Many notions of a random network • Naïve algorithm • Erdos-Renyi random graphs • Scale free networks • Even more specialized?

  4. Random Graphs • Three node motifs • Preserve degree for each node • Four node motifs • Preserve degree for each node • Preserve the number of three node motifs

  5. Example Motif

  6. Method • Using brute force, searched target network for every possible subgraph, counting results • Similarly, searched random network • Motifs are patterns that occur greater or equal number of times in random networks more than 1% of the time.

  7. Results

  8. Results (cont.)

  9. Gene/Neural Net Analysis • The nematode neural net and the gene net both contain similar structures • Feed forward • Bi-fan • Both are information processing networks with sensory and acting components • Sensory neurons/transcription factors regulated by biochemical signals • Motor neurons/structural genes

  10. Food Web Analysis • Food Webs do not show feed-forward motifs • Suggests that direct interaction between species at a separation of two layers selected against (e.g. Omnivores) • Bi-parallel suggests that prey of same predator share prey

  11. Electronic Circuit Analysis • Circuits can be classified by function using network motifs • Circuits from benchmark set showed different motifs for each functional class • Some info processing circuits show similar motifs to biological info processing circuits

  12. Web Analysis • Network of hyperlinks • Many more bidirectional links • Motifs indicate a design that allows the shortest path among sets of related pages

  13. Conclusions • Technique robust to data errors • Motifs can indicate common function • ..or could indicate similar evolutionary constraints • Scalability to other types of networks possible • Scalability to larger subgraphs difficult

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