larger clusters to form, however, this occurs at the ex- pence of smaller clusters. Consequently, the distribution is steeper for longer evolution time. The decrease of the exponent with decreasing evolution time can be also un- derstood by considering the aggregation probability as follows: In order to have the same network structure sta- tistically when the evolution time T is doubled, T → 2 T , one needs to reduce the number of the reconstruction events per time step, i.e., 1 − p → (1 − p ) / 2. This means that the aggregation probability is effectively larger and thus the exponent closer to 5/2. Further comparative analysis of the network effects on the cluster dynamics is given in Fig. 5. Here we also con- sider the case where the underlying tree network remains fixed in the actions, i.e, following the action events only the original links are preserved. It is remarkable that, when the largest cluster starts dominating the dynam- ics (above the threshold value s$_{0}$ ≈ 6 in this case), the tail of the distribution on the tree network coincides with the tail obtained in the annealed random graph topology. This supports our conclusion that the local structure of the network plays a pivotal role in this cluster dynamics. Specifically, the tree graph structure and the annealed random graph, which is locally tree-like, have the same effects statistically on the cluster aggregation and conse- quently on the size of the largest cluster. with a prefactor and different parameters. Specifically, q =1.04 (exponential limit!) for the random graph topol- ogy, and q =1.12 for the fixed tree network. Whereas, a prominent power-law tail with the with the slope τ =2.66, compatible with q =1.38, occurs in the case of the evolution of network. This implies that the units which are deployed less often than the threshold time ( T$_{0}$ ∼ 10 3 steps), appear to be self-organized in a hierar- chical manner. We have studied the cluster aggregation– fragmentation processes on networks and assuming that the largest available cluster is always involved in the fragmentation or action events , which also may affect the network structure. This is motivated by the dynamics of conflicts, where planned war actions deploy the largest forces (and may result in correspondingly large damage). The underlying network with its fixed or dynamically evolving structure represents constraints for the aggregation processes, thus affecting the largest cluster sizes, which is relevant for war conflicts. We also studied the situation where such constraints do not exist Apart from the cluster size distribution, we find that the network structure also plays a role in how often the units participate in the action. The distribution of wait- ing times between successive actions of a unit, averaged over all units on the network, is shown in Fig. 5(top) for the three network topologies. Here we see differences appear between annealed random graph and fixed tree network. Apart from small times, the data can be fitted by the q − exponential function (see [14] for the origin of this distribution in long-range interaction systems): P (Δ t ) = B (Δ t ) $^{α}$[1 + (1 − q )Δ t/T$_{0}$ ] 1 / (1 − q ) , (4) FIG. 5: (top)Distribution of time intervals between consec- utive action events of a particular unit, averaged over all 1000 units, for three network topologies: annealed random graph, fixed network of tree-with-subtrees, and evolving net- work built on the tree-with-subtrees. (bottom) Distribution of sizes of all clusters for the same networks. Fixed aggrega- tion probability p = 0 . 9 and simulation time T = 10 4 steps. FIG. 4: Size distribution of all clusters on the evolving net- work for p =0.9,0.95, 0.98, and evolution time T = 10 5 steps. Full lines indicate slopes τ =6.3,3.8, 3.1, while dashed line has the slope τ = 2 . 5. Inset: Scaling exponent τ plotted against inverse evolution time T for fixed p = 0 . 95. 10 0 10 1 10 2 10 3 s 10 −2 10 −1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 P(s)  p = 0.98  p = 0.95  p = 0.90 10 −6 10 −5 10 −4 10 −3 10 −2 1/T 2 3 4 4 4 10 0 10 1 10 2 10 3 10 4 10 5 t 10 −4 10 −3 10 −2 10 −1 10 0 10 1 10 2 P( t )  aRGN  OriginalNetw  EmergentNetw y=0.08x$^{1.54}$(1+0.38x/118) −4.2 y=18(1+0.1x/680) −8.8  y=0.028x$^{1.2}$(1+0.0381x/260) −19.8 slope: −2.2 10$^{-}$1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 0 10 1 10 2 P(s) s OriginalNetw Slope: 2.5 aRGN EmergentNetw IV. CONCLUSIONS 5