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Graph topological transformations in space-filling cell aggregates
Fig 3
Graph transformation for a T1 transition.
A Graphs in the left and right columns correspond to the initial and final cell configurations, respectively. Gray arrows represent relationships labeled IS_PART_OF. The graph in the middle column shows the graph transformation, which includes green and red relationships, indicating relationship creations and deletions, respectively. Additionally, the graph transformation specifies property values of the newly created relationships. B Schematic of determining the value of contextual property for a new vertex→edge relationship generated between vertex v1 and edge e3 (
). After the transformation, vertex v1 assumes the same role in the context of edge e3 as the role of v2 in the context of e3 before the transformation (s2,3). This occurs because the edge e3 merely replaces v2 (blue) with v1 (red). C Schematic of determining the value of contextual property for a new edge→polygon relationship generated between edge e5 and polygon p1 (
). The calculation of 
(red) relies on one of the vertices of e5, i.e., v2 (green), and the edge linked to both v2 and p1, i.e., e2 (also depicted in green). The assignment of 
is determined based on the contextual properties of: (i) edge e2 in the context of polygon p1, σ2,1, (blue) and (ii) vertex v2 in contexts of edges e2, 
, and e5, 
, (green). In short, the contextual property 
aligns or opposes that of σ2,1 depending on the similarity or dissimilarity of 
and 
.
doi: https://doi.org/10.1371/journal.pcbi.1012089.g003