Simulations of the detailed model for pairwise interactions. 

Dynamic simulations of the flocking model are carried out to visualise group cohesion for different values of the topological neighbourhood (K) for group size, N = 30. We start the simulation with a cohesive group and look at the group dynamics for different K. For K = 1, we can see that the agents break into clusters of sizes 2-3 and drift apart from each other. For K = 3, the group again breaks into clusters, but the number of clusters reduces. For K = 5, the group usually breaks into 2 clusters. Finally, for K greater than 8 (i.e., K ~ 0.3 N), the group remains cohesive most of the time.

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Attraction interaction networks. 

Motion of the group is visualised along with the dynamically changing attraction interaction networks, for group size of N = 10. Here we show the agent's movement in the group centre's reference frame. We can see that for K = 1, the interactions are sparse and limited to the nearest neighbours. Hence, the group breaks and small sub-groups drift away. However, for K = 3, the interaction networks are dense. Therefore, the group remains cohesive as the dense attraction interactions prevent the agents from drifting away.

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Averaging vs Pairwise interactions.

For sufficiently large K, groups with pairwise interaction (where individuals interact with only one of its K neighbours at a time) can achieve the same cohesion as those with averaging interactions (individual interacts with all its K neighbours).