Statistical networks emerging from link-node interactionsA. E. Allahverdyan and K. G. Petrosyan
Yerevan Physics Institute - Alikhanian Brothers Street 2, Yerevan 375036, Armenia
received 13 April 2006; accepted in final form 27 July 2006
published online 23 August 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.
64.60.Cn - Order-disorder transformations; statistical mechanics of model systems.
89.75.Hc - Networks and genealogical trees.
75.10.Hk - Classical spin models.
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