Scale-free network topology and multifractality in a weighted planar stochastic lattice

We propose a weighted planar stochastic lattice (WPSL) formed by the random sequential partition of a plane into contiguous and non-overlapping blocks and we find that it evolves following several non-trivial conservation laws, namely Sigma(N)(i) x(i)(n-1)y(i)(4/n-1) is independent of time for all n, where x(i) and y(i) are the length and width of the ith block. Its dual on the other hand, obtained by replacing each block with a node at its centre and the common border between blocks with an edge joining the two vertices, emerges as a network with a power-law degree distribution P(k) similar to k(-gamma), where gamma = 5.66 reveals scale-free coordination number disorder since P(k) also describes the fraction of blocks having k neighbours. To quantify the size disorder, we show that if the ith block is populated with p(i) similar to x(i)(3), then its distribution in the WPSL exhibits multifractality.