A transition from river networks to scale-free networks

Details A transition from river networks to scale-free networks A transition from river networks to scale-free networks

2007-01-11

arxiv.org/abs/cond-mat/0701246v1

New J. Phys. 9, 30 (2007)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figure

Scientific paper

10.1088/1367-2630/9/2/030

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$ such points the network is grown by including them one by one according to the serial number into the growing network. The $t$-th point is attached to the $i$-th node of the network using the probability: $\pi_i(t) \sim k_i(t)\ell_{ti}^{\alpha}$ where $k_i(t)$ is the degree of the $i$-th node and $\ell_{ti}$ is the Euclidean distance between the points $t$ and $i$. Here $\alpha$ is a continuously tunable parameter and while for $\alpha=0$ one gets the simple Barab\'asi-Albert network, the case for $\alpha \to -\infty$ corresponds to the spatially continuous version of the well known Scheidegger's river network problem. The modulating parameter $\alpha$ is tuned to study the transition between the two different critical behaviors at a specific value $\alpha_c$ which we numerically estimate to be -2.

Affiliated with

Also associated with

No associations

Rating

A transition from river networks to scale-free networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A transition from river networks to scale-free networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A transition from river networks to scale-free networks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-642693