Network Motifs

Zach Saul

CS 289Network 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