Figure 3
From: Tracing patterns and shapes in remittance and migration networks via persistent homology
Examples and non-examples of Simplices. The order on the vertices is preserved by the corresponding simplex name: (a) a 0-simplex \([a]\), (b) a 1-simplex \([a,b]\), (c) a 2-simplex \([a,b,c]\), (d) 3-simplices \([a,b,c,d]\), and \([d,a,b,c]\). (e) and (f) Since not all vertices are connected, the set \(\{a,b,c,d\}\) does not form a 4-clique, and hence is not a 3-simplex. (g) An example of a 3-clique that is not directed since a unique source (nor sink) does not exist. (h) An example of a directed clique complex having four 0-simplices, five 1-simplices, and one 2-simplex