* 4. As shown, the regular graphsPLOS ONE | DOI:10.1371/journal.pone.0126076 May 15,6 /The Role of the Organization Structure in the Diffusion of InnovationsFig 2. Consensus time versus versus the performance of the innovation. Number of steps needed to reach a consensus (either to accept or reject the innovation) as a function of the the initial new method’s performance for the six different topologies considered. By comparing this panels from the curves shown in Fig 1, it can be observed that the values of R* corresponding to the maximum consensus times match the values of R* for which P(acceptance) * 0.5. Other values are N = 1000, R = 1, = 10, = 0.5, m = 0.5, ) R*, = N-1. Each point is averaged over 104 network realizations. doi:10.1371/journal.pone.0126076.g(hierarchical and lattice) show higher acceptance probabilities than the complex networks (ER and BA) and, in turn, ER networks show higher success probabilities than BA graphs. In conclusion, for a given mean connectivity, increasing degree heterogeneity decreases the likelihood that the proposal will be accepted. Furthermore, comparing the two top panels, it can be observed that the size of the system does not have a significant influence on the acceptance probability. Nevertheless, in heterogeneous and star graphs, large system sizes show lower ratios of acceptance. Regarding the effect of the seed size, as can be seen by comparing the curves in the bottom panel which those shown in the up-left panel, the increase of the number of initial adopters has a positive influence on the success probability. Comparing the three panels, we see that it is the amount of initials adopters , not its fraction, that determines the success probability. This is due to the fact that purchase SP600125 achieving a critical mass of adopters in early stages is key to the success of the innovation. This result has important implications because it indicates that the efforts required to spread an innovation are independent of the size of the system. Each panel of Fig 2 represents, for each of the different topologies considered, the time needed to reach global consensus, that is, the number of dynamical steps until all the agents ofPLOS ONE | DOI:10.1371/journal.pone.0126076 May 15,7 /The Role of the Organization Structure in the Diffusion of InnovationsFig 3. Acceptance probability versus learning ratio and social pressure. Fraction of realizations in which the innovation has been adopted P (acceptance) versus the learning ratio m (left panel) and versus the social pressure parameter (right panel) for the six different types of networks studied. The value of R* is chosen so that P(acceptance) * 0.5 for m = 0.5, being R* = 1.55, 2.2, 3.3, 4.5, 35, 155 for the hierarchical, lattice, Erd -R yi, Barab iAlbert, star and complete graphs respectively. Other values are N = 1000, R = 1, = 10, = 0.5, ) R*, = N-1. Each point is averaged over 104 different realizations. See the main text for further details. doi:10.1371/journal.pone.0126076.gthe system shared the same opinion about the innovation. For each structure of the networks of contacts we see how a peak in the PX-478 price transition time is revealed, signaling the existence of a phase transition between the two different final states. In fact, by comparing these results with those shown in the upper-left panel of Fig 1, it can be observed that the values of the innovation performance R?corresponding to the maximum consensus time (the peaks of Fig 2) match the values of R?f.* 4. As shown, the regular graphsPLOS ONE | DOI:10.1371/journal.pone.0126076 May 15,6 /The Role of the Organization Structure in the Diffusion of InnovationsFig 2. Consensus time versus versus the performance of the innovation. Number of steps needed to reach a consensus (either to accept or reject the innovation) as a function of the the initial new method’s performance for the six different topologies considered. By comparing this panels from the curves shown in Fig 1, it can be observed that the values of R* corresponding to the maximum consensus times match the values of R* for which P(acceptance) * 0.5. Other values are N = 1000, R = 1, = 10, = 0.5, m = 0.5, ) R*, = N-1. Each point is averaged over 104 network realizations. doi:10.1371/journal.pone.0126076.g(hierarchical and lattice) show higher acceptance probabilities than the complex networks (ER and BA) and, in turn, ER networks show higher success probabilities than BA graphs. In conclusion, for a given mean connectivity, increasing degree heterogeneity decreases the likelihood that the proposal will be accepted. Furthermore, comparing the two top panels, it can be observed that the size of the system does not have a significant influence on the acceptance probability. Nevertheless, in heterogeneous and star graphs, large system sizes show lower ratios of acceptance. Regarding the effect of the seed size, as can be seen by comparing the curves in the bottom panel which those shown in the up-left panel, the increase of the number of initial adopters has a positive influence on the success probability. Comparing the three panels, we see that it is the amount of initials adopters , not its fraction, that determines the success probability. This is due to the fact that achieving a critical mass of adopters in early stages is key to the success of the innovation. This result has important implications because it indicates that the efforts required to spread an innovation are independent of the size of the system. Each panel of Fig 2 represents, for each of the different topologies considered, the time needed to reach global consensus, that is, the number of dynamical steps until all the agents ofPLOS ONE | DOI:10.1371/journal.pone.0126076 May 15,7 /The Role of the Organization Structure in the Diffusion of InnovationsFig 3. Acceptance probability versus learning ratio and social pressure. Fraction of realizations in which the innovation has been adopted P (acceptance) versus the learning ratio m (left panel) and versus the social pressure parameter (right panel) for the six different types of networks studied. The value of R* is chosen so that P(acceptance) * 0.5 for m = 0.5, being R* = 1.55, 2.2, 3.3, 4.5, 35, 155 for the hierarchical, lattice, Erd -R yi, Barab iAlbert, star and complete graphs respectively. Other values are N = 1000, R = 1, = 10, = 0.5, ) R*, = N-1. Each point is averaged over 104 different realizations. See the main text for further details. doi:10.1371/journal.pone.0126076.gthe system shared the same opinion about the innovation. For each structure of the networks of contacts we see how a peak in the transition time is revealed, signaling the existence of a phase transition between the two different final states. In fact, by comparing these results with those shown in the upper-left panel of Fig 1, it can be observed that the values of the innovation performance R?corresponding to the maximum consensus time (the peaks of Fig 2) match the values of R?f.