https://doi.org/10.1140/epjb/e2006-00051-y
Intrinsic degree-correlations in the static model of scale-free networks
School of Physics and Center for Theoretical Physics, Seoul National University, Seoul, 151-747, Korea
Corresponding author: a kahng@phya.snu.ac.kr
Received:
31
October
2005
Published online:
17
February
2006
We calculate the mean neighboring degree function 
and the mean clustering function C(k) of
vertices with degree k as a function of k in finite scale-free
random networks through the static model. While both are
independent of k when the degree exponent γ≥3, they
show the crossover behavior for 2 < γ< 3 from
k-independent behavior for small k to k-dependent behavior
for large k. The k-dependent behavior is analytically derived.
Such a behavior arises from the prevention of self-loops and
multiple edges between each pair of vertices. The analytic results
are confirmed by numerical simulations. We also compare our
results with those obtained from a growing network model, finding
that they behave differently from each other.
PACS: 89.75.Da – Systems obeying scaling laws / 89.75.Fb – Structure and organization in complex systems / 05.65.+b – Self-organized systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006
