%0 Journal Article %1 Bianconi2003 %A Bianconi, Ginestra %A Capocci, Andrea %D 2003 %I American Physical Society %J Physical Review Letters %K cycles graphs loops networks preferential-attachment scale-free %N 7 %P 078701 %R 10.1103/PhysRevLett.90.078701 %T Number of Loops of Size $h$ in Growing Scale-Free Networks %V 90 %X The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number Nh(t) of loops of size h as a function of the system size. In particular, we have found the analytic expression for the scaling of Nh(t) in the Barabási-Albert (BA) scale-free network. We have performed numerical simulations on the scaling law for Nh(t) in the BA network and in other growing scale-free networks, such as the bosonic network and the aging nodes network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.

@article{Bianconi2003, abstract = {The hierarchical structure of scale-free networks has been investigated focusing on the scaling of the number Nh(t) of loops of size h as a function of the system size. In particular, we have found the analytic expression for the scaling of Nh(t) in the {Barab\'{a}si-Albert} ({BA}) scale-free network. We have performed numerical simulations on the scaling law for Nh(t) in the {BA} network and in other growing scale-free networks, such as the bosonic network and the aging nodes network. We show that in the bosonic network and in the aging node network the phase transitions in the topology of the network are accompained by a change in the scaling of the number of loops with the system size.}, added-at = {2011-08-01T13:18:16.000+0200}, author = {Bianconi, Ginestra and Capocci, Andrea}, biburl = {https://www.bibsonomy.org/bibtex/215fd39601ea342052c2d1d9beaedd59c/rincedd}, doi = {10.1103/PhysRevLett.90.078701}, interhash = {0171628094d96fc9e80658c5467deb91}, intrahash = {15fd39601ea342052c2d1d9beaedd59c}, journal = {Physical Review Letters}, keywords = {cycles graphs loops networks preferential-attachment scale-free}, number = 7, pages = 078701, publisher = {American Physical Society}, timestamp = {2011-08-01T13:18:16.000+0200}, title = {Number of Loops of Size $h$ in Growing {Scale-Free} Networks}, volume = 90, year = 2003 }