DnD Lifting (Graph to Simplicial Complex)

configs/transforms/liftings/graph2simplicial/dnd_lifting.yaml

@@ -0,0 +1,6 @@
+transform_type: 'lifting'
+transform_name: "SimplicialDnDLifting"
+complex_dim: 6
+preserve_edge_attr: False
+signed: True
+feature_lifting: ProjectionSum

modules/transforms/data_transform.py

@@ -15,12 +15,16 @@
 from modules.transforms.liftings.graph2simplicial.clique_lifting import (
     SimplicialCliqueLifting,
 )
+from modules.transforms.liftings.graph2simplicial.dnd_lifting import (
+    SimplicialDnDLifting,
+)
 
 TRANSFORMS = {
     # Graph -> Hypergraph
     "HypergraphKNNLifting": HypergraphKNNLifting,
     # Graph -> Simplicial Complex
     "SimplicialCliqueLifting": SimplicialCliqueLifting,
+    "SimplicialDnDLifting": SimplicialDnDLifting,
     # Graph -> Cell Complex
     "CellCycleLifting": CellCycleLifting,
     # Feature Liftings

modules/transforms/liftings/graph2simplicial/dnd_lifting.py

@@ -0,0 +1,102 @@
+import random
+from itertools import combinations
+
+import networkx as nx
+from toponetx.classes import SimplicialComplex
+from torch_geometric.data import Data
+
+from modules.transforms.liftings.graph2simplicial.base import Graph2SimplicialLifting
+
+
+class SimplicialDnDLifting(Graph2SimplicialLifting):
+    r"""Lifts graphs to simplicial complex domain using a Dungeons & Dragons inspired system.
+
+    Parameters
+    ----------
+    **kwargs : optional
+        Additional arguments for the class.
+    """
+
+    def __init__(self, **kwargs):
+        super().__init__(**kwargs)
+
+    def lift_topology(self, data: Data) -> dict:
+        r"""Lifts the topology of a graph to a simplicial complex using Dungeons & Dragons (D&D) inspired mechanics.
+
+        Parameters
+        ----------
+        data : Data
+            The input data to be lifted.
+
+        Returns
+        -------
+        dict
+            The lifted topology.
+        """
+        graph = self._generate_graph_from_data(data)
+        simplicial_complex = SimplicialComplex()
+
+        characters = self._assign_attributes(graph)
+        simplices = [set() for _ in range(2, self.complex_dim + 1)]
+
+        for node in graph.nodes:
+            simplicial_complex.add_node(node, features=data.x[node])
+
+        for node in graph.nodes:
+            character = characters[node]
+            for k in range(1, self.complex_dim):
+                dice_roll = self._roll_dice(character, k)
+                neighborhood = list(
+                    nx.single_source_shortest_path_length(
+                        graph, node, cutoff=dice_roll
+                    ).keys()
+                )
+                for combination in combinations(neighborhood, k + 1):
+                    simplices[k - 1].add(tuple(sorted(combination)))
+
+        for set_k_simplices in simplices:
+            simplicial_complex.add_simplices_from(list(set_k_simplices))
+
+        return self._get_lifted_topology(simplicial_complex, graph)
+
+    def _assign_attributes(self, graph):
+        """Assign D&D-inspired attributes based on node properties."""
+        degrees = nx.degree_centrality(graph)
+        clustering = nx.clustering(graph)
+        closeness = nx.closeness_centrality(graph)
+        eigenvector = nx.eigenvector_centrality(graph)
+        betweenness = nx.betweenness_centrality(graph)
+        pagerank = nx.pagerank(graph)
+
+        attributes = {}
+        for node in graph.nodes:
+            attributes[node] = {
+                "Degree": degrees[node],
+                "Clustering": clustering[node],
+                "Closeness": closeness[node],
+                "Eigenvector": eigenvector[node],
+                "Betweenness": betweenness[node],
+                "Pagerank": pagerank[node],
+            }
+        return attributes
+
+    def _roll_dice(self, attributes, k):
+        """Simulate a D20 dice roll influenced by node attributes where a different attribute is used based on the simplex level."""
+
+        attribute = None
+        if k == 1:
+            attribute = attributes["Degree"]
+        elif k == 2:
+            attribute = attributes["Clustering"]
+        elif k == 3:
+            attribute = attributes["Closeness"]
+        elif k == 4:
+            attribute = attributes["Eigenvector"]
+        elif k == 5:
+            attribute = attributes["Betweenness"]
+        else:
+            attribute = attributes["Pagerank"]
+
+        base_roll = random.randint(1, 20)
+        modifier = int(attribute * 20)
+        return base_roll + modifier