6 p → 1 with a vanishingly small but finite fragmentation probability, the distribution is expected to approach the classical slope 5/2 of random aggregation–fragmentation processes, however, the cutoff might be different. This limit needs more theoretical consideration, which is left out of the present work. The relation between the net- work connectivity and the role of the largest cluster in the dynamics is also the basis for the observed variation of the scaling exponent of all clusters τ with the evolu- tion time of the network in our model. For a fixed frag- mentation probability (number of reconstruction events per time step), the larger evolution time leads to larger size of the fragmented cluster. Hence the distribution of all clusters is steeper, compared to small evolution time, where the difference between cluster sizes is reduced and thus closer to the processes with random cluster events. Our analysis of temporal features of the system reveals the nature of the process underlying the observed clus- ter size distribution. Namely, systematic network recon- struction following the actions over time leads to a com- plex organization between units which causes them to play different roles (frequencies) in the actions. Despite the temporal correlations, which are caused by the in- volvement of the largest cluster in the events, such inter- nal structure does not occur in the original aggregation– fragmentation model in free space and locally sparse net- works. Thus the network reconstruction via the clus- ter dynamics proposed in our work provides the mech- anism for building an effective structure of units, which has large capacity (in terms of the size of events) and a self-organized internal structure. (e.g., in the herding events in stock market dynamics, where the information is globally available), resulting in an annealed random graph structure. The process is controlled by the aggregation probability p , which may result from another coupled stochastic process, but here it is taken as an external parameter. We find a number of new features, in both the geo- metric and temporal patterns of the process, which can be related to the network topology. In particular, the system is characterized by: The distribution of cluster sizes in the mechanism when the largest cluster is always selected for the action, is conditioned by the local connectivity of the network. Ag- gregation process on trees yields large number of small clusters due to sparse connections on the tree. Lack of large clusters results in the large scaling exponent of the size distribution. Within network terminology, the clus- ter aggregation–fragmentation processes in “free space” leads to a sparse random graph structure with annealed links. Its local structure is also tree-like, leading to sta- tistically similar cluster size distribution as on the fixed tree graphs. On the other hand, on the evolving network which gains new links (cliques) after the action events, the node connectivity is progressively increasing. This allows larger clusters to form, and consequently, smaller scaling exponent of the size distribution, compared to the sparse networks for the same fragmentation proba- bility. In both cases the exponent decreases when the fragmentation probability 1 − p is reduced. In the limit We are grateful to Collaborative Linkage Grant CBP.NR.NRCLG.982968 for partial financial support of this work. We would like to thank V. Priezzhev for help- ful discussions. B.T. also acknowledges support from the program No. P1-0044 (Slovenia) and COST-MP0801 ac- tion “Physics of competition and conflicts”. Acknowledgments [9] L. F. Richardson, Statistics of Deadly Quarrels, eds. Q. Wright and C. C. 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Assoc. 43 , 523 (1948). • non-universal power-laws in the distributions of the sizes of events; the scaling exponents appear to vary with the fragmentation probability and the evolu- tion time (in the case of the evolving network); • long-range temporal correlations in time series rep- resenting fluctuations of the number of clusters; the correlations are intensified on networks whose structure evolves through the action events; • evolution of the internal organization, i.e., connec- tivity and hierarchy between units, as a result of the action events.