Network motifs

Connections or actions between nodes have a property of "direction". A can act on B, B can act on A, or A can act on B and B can act on A. In dialectical terms the latter case would be an interaction or interconnection. Throw in a third node, and the number of possible connection types grows to 13?; add a fourth, and the number jumps to 199. (I'm not sure of the math of this, the numbers are from the article referenced below.)

In a 2002 Science article, "Network Motifs: Simple Building Blocks of Complex Networks" six researchers studied various types of networks, and found "the striking appearance of motifs in networks representing a broad range of natural phenomenon."

The researchers studied various real-world networks, including gene regulation, neurons, food webs, electronic circuits, and the World Wide Web. Out of the range of all of the possible connections types, a small number of connection types -- that is, motifs -- showed up much more frequently than the others. Not all networks, though, have the same motifs. The presence of different motifs in different networks suggests a way of distinguishing types of networks.

"None of the network motifs shared by the food webs matched the motifs found in the gene regulation networks or the World Wide Web. Only one of the food web consensus motifs [their term, consensus motifs are "motifs shared by networks of a given type" - jd] also appeared in the neuronal network. Different motifs were found in electronic circuits with different functions. This suggests that motifs can define broad classes of networks, each with specific types of elementary structures. The motifs reflect the underlying processes that generated each type of network [my emphasis - jd]; for example, food webs evolved to allow a flow of energy from the bottom to the top of the food chains, whereas gene regulation and neuron networks evolve to process information. Information processing seems to give rise to significantly different structures than does energy flow.

Two more observations: (1) "In general, the larger the network is the more significant the motifs tend to become;" and (2) motifs "may be interpreted as structures that arise because of the special constraints under which the network has evolved."

Somehow this concept of "motif" is related to the concept of the "law system" (or, the necessary connections) that govern or constrain the interactions between nodes in the network. Or perhaps they are evidence of the existence of the law system? (These would be in part "the special constraints under which the network has evolved" -- internal constraints, while there are also external or environmental constraints as well?)

jd