Issue
EPL
Volume 83, Number 2, July 2008
Article Number 28006
Number of page(s) 5
Section Interdisciplinary Physics and Related Areas of Science and Technology
DOI http://dx.doi.org/10.1209/0295-5075/83/28006
Published online 03 July 2008
EPL, 83 (2008) 28006
DOI: 10.1209/0295-5075/83/28006

Jamming in weighted scale-free gradient networks

B. Wang1, 2, K. Aihara1, 2 and L. Chen3

1  ERATO Aihara Complexity Modelling Project, JST, Institute of Industrial Science, The University of Tokyo 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, Japan
2  Institute of Industrial Science, The University of Tokyo - Tokyo, Japan
3  Department of Electrical Engineering and Electronics, Osaka Sangyo University - Daito, Osaka, 574-8530, Japan

bwang@aihara.jst.go.jp
aihara@sat.t.u.-tokyo.ac.jp

received 17 March 2008; accepted in final form 4 June 2008; published July 2008
published online 3 July 2008

Abstract
In this paper we investigate the jamming degree in weighted scale-free gradient networks, where the gradient flow is described as the edge weight $w_{ij}=(k_{i}*k_{j})^{\alpha}$, which is related with the end-point degrees of a link, and $\alpha $ can be adjusted to be $\alpha > 0$ or $\alpha < 0$. With the new definition of the jamming coefficient, we numerically calculate the jamming coefficient as a function of $\alpha $, the connectivity $\langle k\rangle $, and the degree exponent $\gamma $. The results indicate that for each $\gamma $, there exists an optimal value of $\alpha ^{*}$, at which the jamming coefficient is minimized. The value of $\alpha ^{*}$ depends on the connectivity $\langle k\rangle $. With the increase of $\langle k\rangle $, $\alpha ^{*}$ shifts from zero to the minimum value we examined. Furthermore, there exists a critical value of $\alpha _{c}$, which is numerically estimated to be about 0.5. Namely, when $\alpha < \alpha _{c}$, a homogeneous network will get a higher level of congestion, otherwise, the opposite will happen.

PACS
89.75.-k - Complex systems.
89.75.Hc - Networks and genealogical trees.
87.23.Ge - Dynamics of social systems.

© EPLA 2008