 
Summary: Network models
Properties common to many largescale networks, independently of
their origin and function:
1 Th d d b t di t ib ti d i1. The degree and betweenness distribution are decreasing
functions, usually powerlaws.
2. The distances scale logarithmically with the network size
scale  free
g y
klog
Nlog
l small world
3. The clustering coefficient does not seem to depend on the
network size, and is larger than the clustering coefficient of
comparable random graphscomparable random graphs
There are two model families proposed to explain these properties:
Small world network models and scalefree network models.
Benchmark 1: regular lattices
Onedimensional lattice: constCconstkNl == ,,
2/1
NLl
