Scale free network model – networks continuously expand by addition of nodes, new nodes prefer to link to highly connected nodes. Examples – new web pages, airport links. Model is preferential attachment – you get a power law distribution. Exponent changes when nodes age, when there are costs associated with attachment. Think high school – people want to hang out with the popular people.
In biology – protein networks – nodes are proteins, links are physical interactions. Yeast interactions get power law distribution. Scale free type of network, high clustering. There are different local growth rules that give effective preferential attachment – even though proteins don’t express preference or have desires, etc.
Proteins with lots of neighbors have preferential attachments. You can look at chart and see older proteins gain more connections. Similar curves for (spelling) nematode worms and (spelling) drosophilla (fruit flies).
Metabolic networks, driven by enzymes, have similar power law/scale free distributions.
How does structure influence function? Flux balance analysis – very complex stuff…
The power laws come from the structure of the network – the metabolic network is scale free, and therefore the flux distribution is therefore scale free.
Analogies: larger the network, smaller the core, a collective network effect.