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- import networkx as nx
- import numpy as np
-
- # from tqdm import tqdm
-
-
- def getSPLengths(G1):
- sp = nx.shortest_path(G1)
- distances = np.zeros((G1.number_of_nodes(), G1.number_of_nodes()))
- for i in sp.keys():
- for j in sp[i].keys():
- distances[i, j] = len(sp[i][j]) - 1
- return distances
-
-
- def getSPGraph(G, edge_weight=None):
- """Transform graph G to its corresponding shortest-paths graph.
-
- Parameters
- ----------
- G : NetworkX graph
- The graph to be tramsformed.
- edge_weight : string
- edge attribute corresponding to the edge weight.
-
- Return
- ------
- S : NetworkX graph
- The shortest-paths graph corresponding to G.
-
- Notes
- ------
- For an input graph G, its corresponding shortest-paths graph S contains the same set of nodes as G, while there exists an edge between all nodes in S which are connected by a walk in G. Every edge in S between two nodes is labeled by the shortest distance between these two nodes.
-
- References
- ----------
- [1] Borgwardt KM, Kriegel HP. Shortest-path kernels on graphs. InData Mining, Fifth IEEE International Conference on 2005 Nov 27 (pp. 8-pp). IEEE.
- """
- return floydTransformation(G, edge_weight=edge_weight)
-
-
- def floydTransformation(G, edge_weight=None):
- """Transform graph G to its corresponding shortest-paths graph using Floyd-transformation.
-
- Parameters
- ----------
- G : NetworkX graph
- The graph to be tramsformed.
- edge_weight : string
- edge attribute corresponding to the edge weight. The default edge weight is bond_type.
-
- Return
- ------
- S : NetworkX graph
- The shortest-paths graph corresponding to G.
-
- References
- ----------
- [1] Borgwardt KM, Kriegel HP. Shortest-path kernels on graphs. InData Mining, Fifth IEEE International Conference on 2005 Nov 27 (pp. 8-pp). IEEE.
- """
- spMatrix = nx.floyd_warshall_numpy(G, weight=edge_weight)
- S = nx.Graph()
- S.add_nodes_from(G.nodes(data=True))
- ns = list(G.nodes())
- for i in range(0, G.number_of_nodes()):
- for j in range(i + 1, G.number_of_nodes()):
- if spMatrix[i, j] != np.inf:
- S.add_edge(ns[i], ns[j], cost=spMatrix[i, j])
- return S
-
-
- def untotterTransformation(G, node_label, edge_label):
- """Transform graph G according to Mahé et al.'s work to filter out tottering patterns of marginalized kernel and tree pattern kernel.
-
- Parameters
- ----------
- G : NetworkX graph
- The graph to be tramsformed.
- node_label : string
- node attribute used as label. The default node label is 'atom'.
- edge_label : string
- edge attribute used as label. The default edge label is 'bond_type'.
-
- Return
- ------
- gt : NetworkX graph
- The transformed graph corresponding to G.
-
- References
- ----------
- [1] Pierre Mahé, Nobuhisa Ueda, Tatsuya Akutsu, Jean-Luc Perret, and Jean-Philippe Vert. Extensions of marginalized graph kernels. In Proceedings of the twenty-first international conference on Machine learning, page 70. ACM, 2004.
- """
- # arrange all graphs in a list
- G = G.to_directed()
- gt = nx.Graph()
- gt.graph = G.graph
- gt.add_nodes_from(G.nodes(data=True))
- for edge in G.edges():
- gt.add_node(edge)
- gt.node[edge].update({node_label: G.node[edge[1]][node_label]})
- gt.add_edge(edge[0], edge)
- gt.edges[edge[0], edge].update({
- edge_label:
- G[edge[0]][edge[1]][edge_label]
- })
- for neighbor in G[edge[1]]:
- if neighbor != edge[0]:
- gt.add_edge(edge, (edge[1], neighbor))
- gt.edges[edge, (edge[1], neighbor)].update({
- edge_label:
- G[edge[1]][neighbor][edge_label]
- })
- # nx.draw_networkx(gt)
- # plt.show()
-
- # relabel nodes using consecutive integers for convenience of kernel calculation.
- gt = nx.convert_node_labels_to_integers(
- gt, first_label=0, label_attribute='label_orignal')
- return gt
-
-
- def direct_product(G1, G2, node_label, edge_label):
- """Return the direct/tensor product of directed graphs G1 and G2.
-
- Parameters
- ----------
- G1, G2 : NetworkX graph
- The original graphs.
- node_label : string
- node attribute used as label. The default node label is 'atom'.
- edge_label : string
- edge attribute used as label. The default edge label is 'bond_type'.
-
- Return
- ------
- gt : NetworkX graph
- The direct product graph of G1 and G2.
-
- Notes
- -----
- This method differs from networkx.tensor_product in that this method only adds nodes and edges in G1 and G2 that have the same labels to the direct product graph.
-
- References
- ----------
- [1] Thomas Gärtner, Peter Flach, and Stefan Wrobel. On graph kernels: Hardness results and efficient alternatives. Learning Theory and Kernel Machines, pages 129–143, 2003.
- """
- # arrange all graphs in a list
- from itertools import product
-
- # G = G.to_directed()
- gt = nx.DiGraph()
- # add nodes
- for u, v in product(G1, G2):
- if G1.nodes[u][node_label] == G2.nodes[v][node_label]:
- gt.add_node((u, v))
- gt.nodes[(u, v)].update({node_label: G1.nodes[u][node_label]})
- # add edges, faster for sparse graphs (no so many edges), which is the most case for now.
- for (u1, v1), (u2, v2) in product(G1.edges, G2.edges):
- if (u1, u2) in gt and (
- v1, v2
- ) in gt and G1.edges[u1, v1][edge_label] == G2.edges[u2,
- v2][edge_label]:
- gt.add_edge((u1, u2), (v1, v2))
- gt.edges[(u1, u2), (v1, v2)].update({
- edge_label:
- G1.edges[u1, v1][edge_label]
- })
-
- # # add edges, faster for dense graphs (a lot of edges, complete graph would be super).
- # for u, v in product(gt, gt):
- # if (u[0], v[0]) in G1.edges and (
- # u[1], v[1]
- # ) in G2.edges and G1.edges[u[0],
- # v[0]][edge_label] == G2.edges[u[1],
- # v[1]][edge_label]:
- # gt.add_edge((u[0], u[1]), (v[0], v[1]))
- # gt.edges[(u[0], u[1]), (v[0], v[1])].update({
- # edge_label:
- # G1.edges[u[0], v[0]][edge_label]
- # })
-
- # relabel nodes using consecutive integers for convenience of kernel calculation.
- # gt = nx.convert_node_labels_to_integers(
- # gt, first_label=0, label_attribute='label_orignal')
- return gt
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