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A transition from river networks to scale-free networks | | A. K. Nandi
; S. S. Manna
; | | Date: |
11 Jan 2007 | | Subject: | Statistical Mechanics | | Abstract: | 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 $alpha o -infty$ 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. | | Source: | arXiv, cond-mat/0701246 | | Services: | Forum | Review | PDF | Favorites | |
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