Implement k_truss algorithm (#19)

* Implement k_truss algorithm

Passes networkx tests

* Split k_truss into core and wrapper versions

* Updates based on feedback

* k_truss not implemented for multigraph

Co-authored-by: Erik Welch <erik.n.welch@gmail.com>

Author: jim22k

graphblas_algorithms/algorithms/__init__.py

@@ -1,3 +1,4 @@
 from .cluster import *
+from .core import *
 from .link_analysis import *
 from .reciprocity import *

graphblas_algorithms/algorithms/core.py

@@ -0,0 +1,46 @@
+from graphblas import Matrix, select, monoid, semiring
+from graphblas_algorithms.classes.graph import to_undirected_graph, Graph
+from graphblas_algorithms.utils import get_all, not_implemented_for
+
+
+def k_truss_core(G, k):
+    # Ignore self-edges
+    S = G.get_property("offdiag")
+
+    if k < 3:
+        # Most implementations consider k < 3 invalid,
+        # but networkx leaves the graph unchanged
+        C = S
+    else:
+        # Remove edges not in k-truss
+        nvals_last = S.nvals
+        # TODO: choose dtype based on max number of triangles
+        plus_pair = semiring.plus_pair["int32"]
+        C = Matrix("int32", S.nrows, S.ncols)
+        while True:
+            C(S.S, replace=True) << plus_pair(S @ S.T)
+            C << select.value(C >= k - 2)
+            if C.nvals == nvals_last:
+                break
+            nvals_last = C.nvals
+            S = C
+
+    # Remove isolate nodes
+    indices, _ = C.reduce_rowwise(monoid.any).to_values()
+    Ktruss = C[indices, indices].new()
+
+    # Convert back to networkx graph with correct node ids
+    keys = G.list_to_keys(indices)
+    key_to_id = dict(zip(keys, range(len(indices))))
+    return Graph.from_graphblas(Ktruss, key_to_id=key_to_id)
+
+
+@not_implemented_for("directed")
+@not_implemented_for("multigraph")
+def k_truss(G, k):
+    G = to_undirected_graph(G, dtype=bool)
+    result = k_truss_core(G, k)
+    return result.to_networkx()
+
+
+__all__ = get_all(__name__)

graphblas_algorithms/algorithms/tests/test_core.py

@@ -0,0 +1,11 @@
+import graphblas as gb
+import networkx as nx
+
+from graphblas_algorithms import (
+    DiGraph,
+    Graph,
+    k_truss,
+)
+from graphblas_algorithms.algorithms import core
+
+from networkx.algorithms.tests.test_core import *  # noqa isort:skip

graphblas_algorithms/classes/_utils.py

@@ -100,6 +100,13 @@ def list_to_ids(self, nodes):
     return [self._key_to_id[key] for key in nodes]
 
 
+def list_to_keys(self, indices):
+    if indices is None:
+        return None
+    id2key = self.id_to_key
+    return [id2key[idx] for idx in indices]
+
+
 def vector_to_dict(self, v, *, mask=None, fillvalue=None):
     if mask is not None:
         if fillvalue is not None and v.nvals < mask.parent.nvals:

graphblas_algorithms/classes/graph.py

@@ -258,6 +258,7 @@ def __init__(self, incoming_graph_data=None, **attr):
     list_to_vector = _utils.list_to_vector
     list_to_mask = _utils.list_to_mask
     list_to_ids = _utils.list_to_ids
+    list_to_keys = _utils.list_to_keys
     matrix_to_dicts = _utils.matrix_to_dicts
     to_networkx = _utils.to_networkx
     vector_to_dict = _utils.vector_to_dict