Evolutional family networks generated by group entry growth mechanism with preferential attachment and their features
Department of Electrical and Electronics Engineering, Facult
Last modified: July 14, 2006
The group-entry growth mechanism with preferential attachment generates a new class of scale free networks, of which exact asymptotic connectivity distribution and generation function are derived. They evolve from aristocratic networks to egalitarian networks with asymptotic power law exponent of M+2 depending on the size M and topology of the constituent groups. The asymptotic connectivity distribution fits very well with numerical simulation even in the region of smaller degrees. Then it is demonstrated small size networks can be analysed to find their growth mechanism parameters using asymptotic connectivity distribution templates in region of smaller degrees, where it is easy to satisfy a statistical level of significance. This approach is believed to develop new search of scale free networks in real worlds. As an example of evolutional family network in the real world, Tokyo Metropolitan Railway Network are analysed.