Network 용어

Degree (k) : The most elementary characteristic of a node is its degree (or connectivity), k, which tells us how many links the node has to other nodes.

 

 

Degree distribution (Pk) : The degree distribution, P(k), gives the probability that a selected node has exactly k links. P(k) is obtained by counting the number of nodes N(k) with k=1,2,..... links and dividing by the total number of nodes N. The degree distribution allows us to distinguish between different cses of networks.

 

Scale-free networks and the degree exponent :
Most biological networks are scale-free,which means that their degree distribution approximates a power law,P(k) ~ k ^(–γ) , where γ is the degree exponent and ~ indicates ‘proportional to’. The value ofγ determines many properties ofthe system. The smaller the value ofγ,the more important the role ofthe hubs is in the network.Whereas for γ>3 the hubs are not relevant, for 2> γ>3 there is a hierarchy ofhubs, with the most connected hub being in contact with a small fraction ofall nodes, and for γ = 2 a hub-and-poke network emerges,with the largest hub being in contact with a large fraction ofall nodes. In general, the unusual properties of scale-free networks are valid only for γ<3,when the dispersion<k>2 ,increases with the number ofnodes (that is, σ diverges), = <k2 > <k2 > – <k>2 ,increases ofthe P(k) distribution,which is defined as σ2 resulting in a series ofunexpected features, such as a high degree ofrobustness against accidental node failures.

 

Network biology: Understanding the cell's functional organization