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leading to a milder dependency of s on N . This phenomenon is akin to phase transitions in physics (Kenna and Berche 2010 ). The crossover or breakpoint point N c may be considered a demarkation point between “small/medium” and “large” groups in a

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] Kenyon , R. , Radin, Ch. , Ren , K. and Sadun , L. , Multipodal structure and phase transitions in large constrained graphs , J. Stat. Phys. , 168 ( 2017 ), no. 2 , 233 - 258 . [6

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with the JCSm values for all groups Thus, by the ‘phase transition’ to a higher aggregation level a significant relation is found between average impact of the publications of a group (the actual impact) and

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The reason of this phase transition may lie in its evolution mechanism. Barabási and Albert observe that a power law degree distribution network is built on the basis of two mechanisms: growth and preferential attachment (Barabási and Albert 1999

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Phase transitions as a persistent feature of groups with leaders in models of opinion formation . Physica A 287 : 631 – 643 10.1016/S0378-4371(00)00398-8 . Knobloch Westerwick , S. , Meng , J. 2009

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Oxford Univerity Press Oxford . Castellano , C , Marsili , M , Vespignani , A 2000 Nonequilibrium phase transition in a model for social influence . Physical Review Letters 85 16 3536

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SCHINAZI, R., On multiple phase transitions for branching Markov chains, J. Statist. Phys. 71 (1993), 507-511. MR 94c :60141 On multiple phase transitions for branching Markov chains J. Statist

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