Figure 1
From: The geometry of suspicious money laundering activities in financial networks
Simplices and geometric simplicial complex. (a) Example of geometric n-simplices for \(n=0\) (vertex), \(n=1\) (edge), \(n=2\) (3-clique including its 2D interior) and \(n=3\) (4-clique including its 3D interior, where the dashed line corresponds to an edge that is hidden by the solid 3-simplex body in 3D). (b) A geometric realization of a simplicial complex associated to a graph represented by black vertices and edges. The faces or 2-simplices, the 3-simplices and higher dimensional simplices are not usually considered for a proper (i.e., one-dimensional) network but can be considered in a higher dimensional approach. (c) Forman–Ricci curvature of an edge e on a one-dimensional approach to networks is calculated in terms of the number of other edges incident to its vertices i and j