Relationships in social networks change over time due to various factors, including mobility, preferences for moral behavior, and the consequent making and breaking of social ties.

We therefore study how these factors affect cooperation in actual collaborative networks, where individuals adaptively move with a certain probability.

We find that individuals preferentially move towards the sites with a high degree, which yields networks with a higher average degree, but at the same time is conducive to cooperation because positions at the hubs are most beneficial in that way.

On the one hand, social mobility thus enhances network reciprocity by generating much more cooperation seeds than the original network, but on the other, it also washes out the network structure and creates well-mixed like conditions if too frequent.

Thus, only with limited mobility is network reciprocity optimally enhanced and can yield best conditions for robust cooperation in social networks.

And we expect optimal conditions for other forms of moral behavior to require the same patterns of moderate social mobility.

W. Li, Z. Chen, J. Wang, L. Jiang, M. Perc, Social mobility and network reciprocity shape cooperation in collaborative networks, Chaos, Solitons & Fractals 170 (2023) 113378.