Predictions of the model. (**A**) Phase transition in the structure of the collaboration network. We plot only the largest cluster in the network. For small *p*, the network is formed by numerous small clusters (*p* = 0.10). At the critical point *p*_{c}, the tipping point, a large cluster emerges, that is, a cluster that contains a substantial fraction of the agents. In the vicinity of the transition, the largest cluster has an almost linear or branched structure (*p* = 0.30). As *p* increases, the largest cluster starts to have loops (*p* = 0.35) and eventually becomes a densely connected cluster containing essentially all nodes in the network (*p* = 0.60). We show results for *q* = 0.5 and *m* = 4, where *m* is the number of agents in a team. (**B**) The transition described in (A) can be characterized by the fraction *S* of nodes that belong to the giant component, the order parameter, and the average size 〈*s*〉 of the other clusters, the susceptibility (*33*). The model displays a second-order percolation transition as the fraction *p* of incumbents increases from 0 to 1. The transition occurs for *p* = *p*_{c}, which coincides with the maximum of 〈*s*〉. Note that *p*_{c} is a decreasing function of *m*. We show results for *q* = 0.5 and *m* = 4 and *m* = 8. (**C**) We display graphically the value of *S* as a function of *p* and *q* for *m* = 4. For any value of *q*, the model displays the percolation transition, and the critical fraction *p*_{c} depends on *q*, defining a percolation line *p*_{c}(*m*,*q*). The critical line *p*_{c}(*m*,*q*) is an increasing function of *q*. Even though the order parameter *S* is an important parameter to quantify the structure of the network, not all points with the same *S*, that is, all points represented with the same color, correspond to fields with identical properties. This result is made clear by the lines of equal *f*_{R}. The upper-right corner of the (*p*,*q*) plane is characterized by *f*_{R} close to one, whereas the lower-left corner corresponds to *f*_{R} close to zero. As we show in , all fields considered have parameter values above the transition line.

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