Figure 1

Simplicial complexes vs networks. The figure shows the advantages of the simplicial compared to a network approach. A co-authorship dataset can be encoded both as a network, and as a simplicial complex (a). It easy to see how the simplicial complex approach are able to capture a richer layouts compared with networks. In fact the three papers [a,b], [a,h], [b,h] are mapped in an empty triangle in the simplicial complex, while the single paper [e,f,g] is represented as a filled triangle. This difference is crucial in the detection of holes in the simplicial complex. In both cases depicted in (b) the cycle [1, 2, 3, 4, 5, 6] is cordless in the network representation, but only in the bottom case it corresponds to meaningful information, and can be considered a homological cycle.