Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-09-04
Phys.Rev.Lett. 93 (2004) 168701
Physics
Condensed Matter
Disordered Systems and Neural Networks
To appear in Phys. Rev. Lett
Scientific paper
10.1103/PhysRevLett.93.168701
We perform the renormalization-group-like numerical analysis of geographically embedded complex networks on the two-dimensional square lattice. At each step of coarsegraining procedure, the four vertices on each $2 \times 2$ square box are merged to a single vertex, resulting in the coarsegrained system of the smaller sizes. Repetition of the process leads to the observation that the coarsegraining procedure does not alter the qualitative characteristics of the original scale-free network, which opens the possibility of subtracting a smaller network from the original network without destroying the important structural properties. The implication of the result is also suggested in the context of the recent study of the human brain functional network.
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