Fig 1.
Visual representations of the two most common ways to mathematically model higher-order interactions: simplicial sets and hypergraphs.
In Fig 1a the 0-simplices are the black circles, the 1-simplices are two black circles connected by a black line, and the 2-simplices are three black circles connected by black lines and an orange triangle. In Fig 1b the black circles represent nodes/vertices in the hypergraph and the shaded areas represent the hyperedges that connect them. Note that the two panels do not illustrate the same social structure.
Fig 2.
The graphical representation of how simplicial sets can model the example of the three scenarios of students working on a group project: meeting pairwise, meeting all together, and meeting all together with independent pairwise communication between two members.
Note Fig 2a is how a network would represent all three scenarios.
Fig 3.
Visual examples of learning and discovery rules applied to hypothetical social interactions in humans.
These multibody social interactions could be represented as either simplicial sets or hypergraphs.
Fig 4.
An example of an interference discovery rule where person 1 knows ‘A’ and person 2 knows ‘B’, then after interacting both people discover ‘C’, but no longer know (or are certain of) ‘A’ and ‘B’ respectively.
Table 1.
Evaluates features 2-5 for the example learning rules. indicated the rule can be found in S1 File.
Table 2.
Evaluates features 2-5 for the example discovery rules. * indicated the rule can be found in S1 File.
Fig 5.
Example application of four learning rules to a simplified hypothetical simplicial set containing a 3-simplex and three 2-simplices.
Fig 6.
Example application of three discovery rules to a simplified hypothetical simplicial set containing a 3-simplex and three 2-simplices.