We introduce a growing network model which generates both modular and hierarchical structure in a self-organized way. To this end, we modify the Barabási–Albert model into the one evolving under the principles of division and independence as well as growth and preferential attachment (PA). A...

The problem of close-packed dimers on the honeycomb lattice was solved by Kasteleyn in 1963. Here we extend the solution to include interactions between neighboring dimers in two spatial lattice directions. The solution is obtained by using the method of Bethe ansatz and by converting the dimer...

Owing to the recent progress in high-throughput experimental techniques, the datasets of large-scale protein interactions of prototypical multicellular species, the nematode worm Caenorhabditis elegans and the fruit fly Drosophila melanogaster, have been assayed. The datasets are obtained mainly...

Avalanche dynamics is an indispensable feature of complex systems. Here, we study the self-organized critical dynamics of avalanches on scale-free networks with degree exponent γ through the Bak–Tang–Wiesenfeld (BTW) sandpile model. The threshold height of a node i is set as ki1−η with...

We study avalanche dynamics on scale-free networks, following a power-law degree distribution, pd(k)∼k-γ, through the Bak–Tang–Wiesenfeld sandpile model. The threshold height of a node i is set to be ki1-η with 0⩽η1. We obtain the exponents for the avalanche size and the duration...

In scale-free networks, the degree distribution follows a power law with the exponent γ. Many model networks exist which reproduce the scale-free nature of the real-world networks. In most of these models, the value of γ is continuously tunable, thus is not universal. We study a problem of...