Statistical networks emerging from link-node interactions

A.E. Allahverdyan and K.G. Petrosyan
Europhys. Lett. 75, pp. 908–914, 2006.

We present a network model, where the nodes and links are interacting statistical variables. Each node can be in one of two states (Ising variable), the like nodes tend to link, while the linked nodes tend to be in the same state. The network structure is determined by an effective potential generated by the quickly relaxing nodes, and is measurable via the statistical features of the nodes. For low temperatures the nodes get spontaneously ordered inducing the connectivity enhancement, link-link correlations and clustering. The giant component of the network does appear via a first-order percolation transition leading to bistability and hysteresis.

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