PMID- 30780369
OWN - NLM
STAT- PubMed-not-MEDLINE
DCOM- 20190226
LR  - 20190226
IS  - 2470-0053 (Electronic)
IS  - 2470-0045 (Linking)
VI  - 99
IP  - 1-1
DP  - 2019 Jan
TI  - Self-avoiding walks and connective constants in clustered scale-free networks.
PG  - 012314
LID - 10.1103/PhysRevE.99.012314 [doi]
AB  - Various types of walks on complex networks have been used in recent years to 
      model search and navigation in several kinds of systems, with particular emphasis 
      on random walks. This gives valuable information on network properties, but 
      self-avoiding walks (SAWs) may be more suitable than unrestricted random walks to 
      study long-distance characteristics of complex systems. Here we study SAWs in 
      clustered scale-free networks, characterized by a degree distribution of the form 
      P(k) approximately k;-gamma for large k. Clustering is introduced in these networks by inserting 
      three-node loops (triangles). The long-distance behavior of SAWs gives us 
      information on asymptotic characteristics of such networks. The number of 
      self-avoiding walks, a_n, has been obtained by direct enumeration, allowing us 
      to determine the connective constant mu of these networks as the large-n limit of 
      the ratio a_n/a_n-1. An analytical approach is presented to account for the 
      results derived from walk enumeration, and both methods give results agreeing 
      with each other. In general, the average number of SAWs a_n is larger for 
      clustered networks than for unclustered ones with the same degree distribution. 
      The asymptotic limit of the connective constant for large system size N depends 
      on the exponent gamma of the degree distribution: For gamma>3, mu converges to a finite 
      value as N-->infinity; for gamma=3, the size-dependent mu_N diverges as lnN, and for gamma<3 we 
      have mu_N approximately N;(3-gamma)/2.
FAU - Herrero, Carlos P
AU  - Herrero CP
AD  - Instituto de Ciencia de Materiales, Consejo Superior de Investigaciones 
      Cientificas (CSIC), Campus de Cantoblanco, 28049 Madrid, Spain.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - Phys Rev E
JT  - Physical review. E
JID - 101676019
EDAT- 2019/02/20 06:00
MHDA- 2019/02/20 06:01
CRDT- 2019/02/21 06:00
PHST- 2018/10/29 00:00 [received]
PHST- 2019/02/21 06:00 [entrez]
PHST- 2019/02/20 06:00 [pubmed]
PHST- 2019/02/20 06:01 [medline]
AID - 10.1103/PhysRevE.99.012314 [doi]
PST - ppublish
SO  - Phys Rev E. 2019 Jan;99(1-1):012314. doi: 10.1103/PhysRevE.99.012314.