We study the communication dynamics of Blog networks, focusing on the Russian section of LiveJournal as a case study. Communications (blogger-to-blogger links) in such online communication networks are very dynamic: over 60% of the links in the network are new from one week to the next, though the set of bloggers remains approximately constant. Two fundamental questions are: (i) what models adequately describe such dynamic communication behavior; (ii) how does one detect changes in the nature of the communication dynamics. We approach these questions through the notion of stable statistics. We give strong experimental evidence for the fact that, despite the extreme amount of communication dynamics, several non-trivial aggregate statistics are remarkably stable. We use stable statistics to test our models of communication dynamics: any good model should produce values for these statistics which are both stable and close to the observed ones. Stable statistics can also be used to identify phase transitions, since any change in a normally stable statistic indicates a substantial change in the nature of the communication dynamics.Our model for the communication dynamics in large social networks is based on the locality of communication: a node's communication energy is spent mostly within it's local social "area." By varying the definition of a nodes' social area, our model can be used for a variety of social networks. Our results with different definitions of locality show that the best approximation to the stable statistics observed on the blog network supported by LiveJournal occurs when the social locality is defined as the union of clusters (social groups) containing the node, and when nodes communicate within their locality using a preferential attachment strategy.