TY - JOUR
T1 - Power-Law Behavior in Geometric Characteristics of Full Binary Trees
AU - Paik, Kyungrock
AU - Kumar, Praveen
N1 - Funding Information:
Acknowledgements This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number 2010-0006636). The second author’s time has been partially supported by NSF grant ATM 06-28687.
PY - 2011/2
Y1 - 2011/2
N2 - Natural river networks exhibit regular scaling laws in their topological organization. Here, we investigate whether these scaling laws are unique characteristics of river networks or can be applicable to general binary tree networks. We generate numerous binary trees, ranging from purely ordered trees to completely random trees. For each generated binary tree, we analyze whether the tree exhibits any scaling property found in river networks, i. e., the power-laws in the size distribution, the length distribution, the distance-load relationship, and the power spectrum of width function. We found that partially random trees generated on the basis of two distinct types of deterministic trees, i. e., deterministic critical and supercritical trees, show contrasting characteristics. Partially random trees generated on the basis of deterministic critical trees exhibit all power-law characteristics investigated in this study with their fitted exponents close to the values observed in natural river networks over a wide range of random-degree. On the other hand, partially random trees generated on the basis of deterministic supercritical trees rarely follow scaling laws of river networks.
AB - Natural river networks exhibit regular scaling laws in their topological organization. Here, we investigate whether these scaling laws are unique characteristics of river networks or can be applicable to general binary tree networks. We generate numerous binary trees, ranging from purely ordered trees to completely random trees. For each generated binary tree, we analyze whether the tree exhibits any scaling property found in river networks, i. e., the power-laws in the size distribution, the length distribution, the distance-load relationship, and the power spectrum of width function. We found that partially random trees generated on the basis of two distinct types of deterministic trees, i. e., deterministic critical and supercritical trees, show contrasting characteristics. Partially random trees generated on the basis of deterministic critical trees exhibit all power-law characteristics investigated in this study with their fitted exponents close to the values observed in natural river networks over a wide range of random-degree. On the other hand, partially random trees generated on the basis of deterministic supercritical trees rarely follow scaling laws of river networks.
KW - Binary tree
KW - Complex network
KW - Fractals
KW - Hack's law
KW - Network topology
KW - Self-similarity
UR - http://www.scopus.com/inward/record.url?scp=79951513031&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79951513031&partnerID=8YFLogxK
U2 - 10.1007/s10955-011-0125-y
DO - 10.1007/s10955-011-0125-y
M3 - Article
AN - SCOPUS:79951513031
SN - 0022-4715
VL - 142
SP - 862
EP - 878
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 4
ER -