Network Motifs Zach Saul CS 289 Network Motifs

Network Models • Interactions are represented as directed nodes (as presented in class) •

Network Motifs • Patterns that appear more often in real networks than in randomly

Random Graphs • Three node motifs – Preserve degree for each node • Four

Method • Using brute force, searched target network for every possible subgraph, counting results

Gene/Neural Net Analysis • The nematode neural net and the gene net both contain

Food Web Analysis • Food Webs do not show feed-forward motifs – Suggests that

Electronic Circuit Analysis • Circuits can be classified by function using network motifs •

Web Analysis • Network of hyperlinks • Many more bidirectional links • Motifs indicate

Conclusions • Technique robust to data errors • Motifs can indicate common function •

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

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

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?

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

Example Motif

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.

Results

Results (cont. )

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

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

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

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

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