DnD Lifting (Graph to Simplicial)

The DnD lifting introduces a novel, non-deterministic, and somewhat lighthearted approach to transforming graphs into simplicial complexes. Inspired by the game mechanics of Dungeons & Dragons (D&D), this method incorporates elements of randomness and character attributes to determine the formation of simplices. This lifting aims to add an element of whimsy and unpredictability to the graph-to-simplicial complex transformation process, while still providing a serious and fully functional methodology.

Each vertex in the graph is assigned the following attributes: degree centrality, clustering coefficient, closeness centrality, eigenvector centrality, betweenness centrality, and pagerank. Simplices are created based on the neighborhood within a distance determined by a D20 dice roll + the attribute value. The randomness from the dice roll, modified by the node's attributes, ensures a non-deterministic process for each lifting. The dice roll is influenced by different attributes based on the level of the simplex being formed. The different attributes for different levels of simplices are used in the order shown above, based on the role of those attributes in the context of the graph structure.

From https://github.com/pyt-team/challenge-icml-2024/pull/11