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netmotifs - Network Motifs Simple Building Blocks of...

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Network Motifs: Simple Building Blocks of Complex Networks Milo et al., Science, 2002.
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Beyond Degree Distribution & Diameter Network Motifs: Consider all possible ways to connect 3 nodes with directed edges: (Milo et al., Science , 2002)
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Finding Over-represented Subgraphs For each possible motif M : Let c M be the number of times M occurs in graph G . Estimate p M = Pr[# occurrences c M ] when edges are shuffled. Output M if p M < 0.01 and c M > 4. To generate a random graph for the 3-node motifs: a b c d a b c d a b c d a b c d Single and double edges swapped separately:
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To Generate Random Graphs With a Given Distribution of (n-1)-node subgraphs: Define an “energy” on a vector of occurrences of motifs: Energy( V rand ) = M | V real ,M V rand ,M | ( V real ,M V rand ,M ) When V rand = V real , the energy is 0. Start with a randomized network. Until Energy is small: Make a random swap. If the swap reduces the energy, keep it Otherwise, keep it with probability exp(- Δ E/T) +
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I I I E “Information processing” networks tend to use the same motifs Other networks each had their own distinct collection of motifs. Feed forward, e.g.: filter out transient signals. (Milo et al., Science , 2002)
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Quickly Finding Motifs 858L
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Network Motif Discovery Using Subgraph Enumeration and Symmetry-Breaking Grochow & Kellis, RECOMB 2007
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