Theory of complex networks applies to many problems in sociology and economy. Most networks are considered to result from a growth process. However, some networks can also rearrange their structure in a sort of thermalization processes. Such processes lead to a class of networks, whose statistical properties can be quite different from those observed for growing networks. In this talk I would like to discuss a simple model of homogeneous network, where the homogeneity is forced by rewiring. Although some properties are similar to those of growing networks, some others like for instance the distance distribution are different. As I will argue, it is related to the lack of causal ordering of nodes.

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