Create utility function GraphDimension, which, given a causal graph, a method for estimation, and a pair of vertices in the graph, will return an estimate for the dimension of the graph.
Currently, the method supported is FlatCausalDiamondRelationProbability, which is based on the Myrheim-Meyer dimension estimation algorithm. This method comes from Causal Set Theory and works by counting the number of causal relations and events in an interval of the graph defined as the intersection of the past of one event with the future of another (making use of AcyclicGraphTake). A ratio between said number of events and number of relations is a function solely of the dimension of the manifold into which the causal graph embeds. Thus, GraphDimension solves this expression of dimension (which can be found in GraphDimension.md), returning the estimation value.
Comments
In the FlatCausalDiamondRelationProbability method, if the events (vertices) provided are causally disconnected or are the same event, the function will return infinity.
Changes
GraphDimension, which, given a causal graph, a method for estimation, and a pair of vertices in the graph, will return an estimate for the dimension of the graph.FlatCausalDiamondRelationProbability, which is based on the Myrheim-Meyer dimension estimation algorithm. This method comes from Causal Set Theory and works by counting the number of causal relations and events in an interval of the graph defined as the intersection of the past of one event with the future of another (making use ofAcyclicGraphTake). A ratio between said number of events and number of relations is a function solely of the dimension of the manifold into which the causal graph embeds. Thus,GraphDimensionsolves this expression of dimension (which can be found in GraphDimension.md), returning the estimation value.Comments
FlatCausalDiamondRelationProbabilitymethod, if the events (vertices) provided are causally disconnected or are the same event, the function will return infinity.This change is