Examples Hierarchical network model

1 examples

1.1 actor network
1.2 language network
1.3 network of webpages
1.4 domain network

examples
actor network

based on actor database available @ www.imdb.com network defined hollywood actors connected each other if both appeared in same movie, resulting in data set of 392,340 nodes , 15,347,957 edges. earlier studies have shown, network exhibits scale-free properties @ least high values of k. moreover, clustering coefficients seem follow required scaling law parameter -1 providing evidence hierarchical topology of network. intuitively, one-performance actors have definition clustering coefficient of 1 while actors starring in several movies highly unlikely work same crew in general results in decreasing clustering coefficient number of co-stars grows.

language network

words can regarded network if 1 specifies linkage criteria between them. defining links appearance synonym in merriam-webster dictionary semantic web of 182,853 nodes 317,658 edges constructed. turned out, obtained network of words indeed follows power law in degree distribution while distribution of clustering coefficient indicates underlying web follows hierarchical structure γ=3.25 , β=1.

network of webpages

by mapping www.nd.edu domain network of 325,729 nodes , 1,497,135 edges obtained degree distribution followed power law γout=2.45 , γin=2.1 out- , in-degrees, respectively. evidence scaling law distribution of clustering coefficients weaker in previous cases although there visible declining pattern in distribution of c(k) indicating more links domain has less interconnected linked/linking web pages are.

domain network

the domain network, i.e. internet @ autonomous system (as) level administrative domains said connected in case there router connects them, found comprise 65,520 nodes , 24,412 links between them , exhibit properties of scale-free network. sample distribution of clustering coefficients fitted scaling function c(k)~k exponent (in absolute terms) smaller theoretical parameter deterministic scale-free networks.