graph_edit_distance

graph_edit_distance(G1, G2, node_match=None, edge_match=None, node_subst_cost=None, node_del_cost=None, node_ins_cost=None, edge_subst_cost=None, edge_del_cost=None, edge_ins_cost=None, roots=None, upper_bound=None, timeout=None)

Returns GED (graph edit distance) between graphs G1 and G2.

Graph edit distance is a graph similarity measure analogous to Levenshtein distance for strings. It is defined as minimum cost of edit path (sequence of node and edge edit operations) transforming graph G1 to graph isomorphic to G2.

Parameters

G1, G2: graphs

The two graphs G1 and G2 must be of the same type.

node_matchcallable

A function that returns True if node n1 in G1 and n2 in G2 should be considered equal during matching.

The function will be called like

node_match(G1.nodes[n1], G2.nodes[n2]).

That is, the function will receive the node attribute dictionaries for n1 and n2 as inputs.

Ignored if node_subst_cost is specified. If neither node_match nor node_subst_cost are specified then node attributes are not considered.

edge_matchcallable

A function that returns True if the edge attribute dictionaries for the pair of nodes (u1, v1) in G1 and (u2, v2) in G2 should be considered equal during matching.

The function will be called like

edge_match(G1[u1][v1], G2[u2][v2]).

That is, the function will receive the edge attribute dictionaries of the edges under consideration.

Ignored if edge_subst_cost is specified. If neither edge_match nor edge_subst_cost are specified then edge attributes are not considered.

node_subst_cost, node_del_cost, node_ins_costcallable

Functions that return the costs of node substitution, node deletion, and node insertion, respectively.

The functions will be called like

node_subst_cost(G1.nodes[n1], G2.nodes[n2]), node_del_cost(G1.nodes[n1]), node_ins_cost(G2.nodes[n2]).

That is, the functions will receive the node attribute dictionaries as inputs. The functions are expected to return positive numeric values.

Function node_subst_cost overrides node_match if specified. If neither node_match nor node_subst_cost are specified then default node substitution cost of 0 is used (node attributes are not considered during matching).

If node_del_cost is not specified then default node deletion cost of 1 is used. If node_ins_cost is not specified then default node insertion cost of 1 is used.

edge_subst_cost, edge_del_cost, edge_ins_costcallable

Functions that return the costs of edge substitution, edge deletion, and edge insertion, respectively.

The functions will be called like

edge_subst_cost(G1[u1][v1], G2[u2][v2]), edge_del_cost(G1[u1][v1]), edge_ins_cost(G2[u2][v2]).

That is, the functions will receive the edge attribute dictionaries as inputs. The functions are expected to return positive numeric values.

Function edge_subst_cost overrides edge_match if specified. If neither edge_match nor edge_subst_cost are specified then default edge substitution cost of 0 is used (edge attributes are not considered during matching).

If edge_del_cost is not specified then default edge deletion cost of 1 is used. If edge_ins_cost is not specified then default edge insertion cost of 1 is used.

roots2-tuple

Tuple where first element is a node in G1 and the second is a node in G2. These nodes are forced to be matched in the comparison to allow comparison between rooted graphs.

upper_boundnumeric

Maximum edit distance to consider. Return None if no edit distance under or equal to upper_bound exists.

timeoutnumeric

Maximum number of seconds to execute. After timeout is met, the current best GED is returned.

See also

optimal_edit_paths, optimize_graph_edit_distance

is_isomorphic

test for graph edit distance of 0

References

1

Zeina Abu-Aisheh, Romain Raveaux, Jean-Yves Ramel, Patrick Martineau. An Exact Graph Edit Distance Algorithm for Solving Pattern Recognition Problems. 4th International Conference on Pattern Recognition Applications and Methods 2015, Jan 2015, Lisbon, Portugal. 2015, <10.5220/0005209202710278>. <hal-01168816> https://hal.archives-ouvertes.fr/hal-01168816

Examples

>>> G1 = nx.cycle_graph(6)
>>> G2 = nx.wheel_graph(7)
>>> nx.graph_edit_distance(G1, G2)
7.0

>>> G1 = nx.star_graph(5)
>>> G2 = nx.star_graph(5)
>>> nx.graph_edit_distance(G1, G2, roots=(0, 0))
0.0
>>> nx.graph_edit_distance(G1, G2, roots=(1, 0))
8.0