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Functions for hashing graphs to strings.
Isomorphic graphs should be assigned identical hashes.
For now, only Weisfeiler-Lehman hashing is implemented.
The function iteratively aggregates and hashes neighborhoods of each node.
After each node’s neighbors are hashed to obtain updated node labels,
a hashed histogram of resulting labels is returned as the final hash.
Hashes are identical for isomorphic graphs and strong guarantees that
non-isomorphic graphs will get different hashes. See [1]_ for details.
If no node or edge attributes are provided, the degree of each node
is used as its initial label.
Otherwise, node and/or edge labels are used to compute the hash.
Parameters:
G – graph
The graph to be hashed.
Can have node and/or edge attributes. Can also have no attributes.
edge_attr – string, default=None
The key in edge attribute dictionary to be used for hashing.
If None, edge labels are ignored.
node_attr – string, default=None
The key in node attribute dictionary to be used for hashing.
If None, and no edge_attr given, use the degrees of the nodes as labels.
iterations – int, default=3
Number of neighbor aggregations to perform.
Should be larger for larger graphs.
digest_size – int, default=16
Size (in bits) of blake2b hash digest to use for hashing node labels.
Returns:
string
Hexadecimal string corresponding to hash of the input graph.
Return type:
h
Notes
To return the WL hashes of each subgraph of a graph, use
weisfeiler_lehman_subgraph_hashes
Similarity between hashes does not imply similarity between graphs.
The dictionary is keyed by node to a list of hashes in increasingly
sized induced subgraphs containing the nodes within 2*k edges
of the key node for increasing integer k until all nodes are included.
The function iteratively aggregates and hashes neighborhoods of each node.
This is achieved for each step by replacing for each node its label from
the previous iteration with its hashed 1-hop neighborhood aggregate.
The new node label is then appended to a list of node labels for each
node.
To aggregate neighborhoods at each step for a node $n$, all labels of
nodes adjacent to $n$ are concatenated. If the edge_attr parameter is set,
labels for each neighboring node are prefixed with the value of this attribute
along the connecting edge from this neighbor to node $n$. The resulting string
is then hashed to compress this information into a fixed digest size.
Thus, at the $i$th iteration nodes within $2i$ distance influence any given
hashed node label. We can therefore say that at depth $i$ for node $n$
we have a hash for a subgraph induced by the $2i$-hop neighborhood of $n$.
Can be used to to create general Weisfeiler-Lehman graph kernels, or
generate features for graphs or nodes, for example to generate ‘words’ in a
graph as seen in the ‘graph2vec’ algorithm.
See [1]_ & [2]_ respectively for details.
Hashes are identical for isomorphic subgraphs and there exist strong
guarantees that non-isomorphic graphs will get different hashes.
See [1]_ for details.
If no node or edge attributes are provided, the degree of each node
is used as its initial label.
Otherwise, node and/or edge labels are used to compute the hash.
Parameters:
G – graph
The graph to be hashed.
Can have node and/or edge attributes. Can also have no attributes.
edge_attr – string, default=None
The key in edge attribute dictionary to be used for hashing.
If None, edge labels are ignored.
node_attr – string, default=None
The key in node attribute dictionary to be used for hashing.
If None, and no edge_attr given, use the degrees of the nodes as labels.
iterations – int, default=3
Number of neighbor aggregations to perform.
Should be larger for larger graphs.
digest_size – int, default=16
Size (in bits) of blake2b hash digest to use for hashing node labels.
The default size is 16 bits
Returns:
dict
A dictionary with each key given by a node in G, and each value given
by the subgraph hashes in order of depth from the key node.
Return type:
node_subgraph_hashes
Notes
To hash the full graph when subgraph hashes are not needed, use
weisfeiler_lehman_graph_hash for efficiency.
Similarity between hashes does not imply similarity between graphs.