Figure 4

Results with alternative random-graph algorithms. Networks generated using the Barabási-Albert (BA) algorithm and the Watts-Strogatz (WS) algorithm are shown for different parameter values. The WS networks generated were generated from \({\boldsymbol{k}}={\boldsymbol{1}}\) and \({\boldsymbol{k}}={\boldsymbol{2}}\) connected nearest neighbors on each side initially. The plots are for networks in the small-world region of \({\boldsymbol{p}}={\boldsymbol{0}}{\boldsymbol{.}}\,{\boldsymbol{5}}\). The BA algorithm was used to generate networks starting from \({{\boldsymbol{m}}}_{{\boldsymbol{0}}}={\boldsymbol{2}}\) nodes and adding each node connected to \({\boldsymbol{m}}\) existing nodes. Typically, \({{\boldsymbol{m}}}_{{\boldsymbol{0}}}={\boldsymbol{m}}\), which is the m = 2 case shown here. It drops to zero very quickly. The \({\boldsymbol{m}}={\boldsymbol{1}}\) case remains very similar to the star topology as each new node only forms one link most probably to the same node. This allows for a higher probability of synchronization up to higher network sizes.