Networkx algorithms for maximum common ordered subtree minors (or embedding) and maximum common subtree isomorphism. Contains pure python and cython optimized versions.
At its core the maximum_common_ordered_subtree_embedding function is an implementation of:
Lozano, Antoni, and Gabriel Valiente.
"On the maximum common embedded subtree problem for ordered trees."
String Algorithmics (2004): 155-170.
https://pdfs.semanticscholar.org/0b6e/061af02353f7d9b887f9a378be70be64d165.pdfAnd maximum_common_ordered_subtree_isomorphism is a variant of the above algorithm that returns common subtree ismorphism instead of subtree minors.
Demo
Consider two directed ordered trees (the algorithm also works on undirected ordered trees):
>>> import networkx as nx
>>> tree1 = nx.DiGraph()
>>> tree2 = nx.DiGraph()
>>> tree1.add_edges_from([(0, 2), (5, 7), (5, 4), (5, 3), (2, 5), (2, 6), (3, 1)])
>>> tree2.add_edges_from([(0, 6), (0, 1), (1, 5), (6, 2), (5, 4), (5, 3), (5, 7)])
>>> print('Tree 1:')
>>> nx.write_network_text(tree1)
>>> print('Tree 2:')
>>> nx.write_network_text(tree2)
Tree 1:
╙── 0
└─╼ 2
├─╼ 5
│ ├─╼ 7
│ ├─╼ 4
│ └─╼ 3
│ └─╼ 1
└─╼ 6
Tree 2:
╙── 0
├─╼ 6
│ └─╼ 2
└─╼ 1
└─╼ 5
├─╼ 4
├─╼ 3
└─╼ 7The maximum common ordered isomorphism (a strict common subtree structure) is:
>>> import networkx_algo_common_subtree
>>> subtree1, subtree2, score = networkx_algo_common_subtree.maximum_common_ordered_subtree_isomorphism(tree1, tree2)
>>> print(f'{score=}')
>>> print('Isomorphic Subtree 1:')
>>> nx.write_network_text(subtree1)
>>> print('Isomorphic Subtree 2:')
>>> nx.write_network_text(subtree2)
score=3
Isomorphic Subtree 1:
╙── 5
├─╼ 4
└─╼ 3
Isomorphic Subtree 2:
╙── 5
├─╼ 4
└─╼ 3The biggest common structure between both of the original trees is the subtree involving 5, 3, 4. Notice that the (5, 7) edge is not included because these are ordered subtrees. In tree 1, the (5, 7) edge is before the (5, 4) edge and in the second it is after it, so it is not included because the edges are not in the same order.
This substructure can be generalized by allowing edges in the original graphs to be collapsed, which can produce larger common substructures. This is the maximum common ordered embedding.
>>> import networkx_algo_common_subtree
>>> subtree1, subtree2, score = networkx_algo_common_subtree.maximum_common_ordered_subtree_embedding(tree1, tree2)
>>> print(f'{score=}')
>>> print('Embedded Subtree 1:')
>>> nx.write_network_text(subtree1)
>>> print('Embedded Subtree 2:')
>>> nx.write_network_text(subtree2)
score=4
Embedded Subtree 1:
╙── 0
└─╼ 5
├─╼ 4
└─╼ 3
Embedded Subtree 2:
╙── 0
└─╼ 5
├─╼ 4
└─╼ 3In this example, the edges (0, 2) and (2, 5) in first tree were collapsed into (0, 5). Similarly in the second tree the edges (0, 1) and (1, 5) were collapsed into (0, 5), thus increasing the size of the common ordered subtree.
Other Information
Standalone versions of code were originally submitted as PRs to networkx proper:
https://github.com/networkx/networkx/pull/4350 https://github.com/networkx/networkx/pull/4327
However, these algorithms are roughly O(N⁴), they require a a fast binary (e.g. C / cython) implementation to work on graphs of reasonable size. Thus they are unlikely to be added to mainline networkx.
These algorithms are components of algorithms in torch_liberator, see related information:
TorchLiberator |
|
Torch Hackathon 2021 |
1 maintainer
Release files for networkx-algo-common-subtree 0.2.2
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No |
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Release files / networkx_algo_common_subtree-0.2.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp310-cp310-manylinux_2_17_x86_64.manylinux2014_x86_64.whl |
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| Size | 168.1 kB |
| Tags | CPython 3.10 Linux glibc 2.17+ x86-64 |
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No |
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Release files / networkx_algo_common_subtree-0.2.2-cp310-cp310-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp310-cp310-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl |
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| Size | 170.3 kB |
| Tags | CPython 3.10 Linux glibc 2.17+ x86-32 Linux glibc 2.5+ x86-32 |
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No |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp310-cp310-macosx_11_0_arm64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp310-cp310-macosx_11_0_arm64.whl |
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| Size | 136.0 kB |
| Tags | CPython 3.10 macOS 11.0+ ARM64 |
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No |
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Release files / networkx_algo_common_subtree-0.2.2-cp39-cp39-win_amd64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp39-cp39-win_amd64.whl |
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| Size | 130.0 kB |
| Tags | CPython 3.9 Windows x86-64 |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp39-cp39-musllinux_1_2_x86_64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp39-cp39-musllinux_1_2_x86_64.whl |
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| Size | 171.3 kB |
| Tags | CPython 3.9 Linux musl 1.2+ x86-64 |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp39-cp39-musllinux_1_2_i686.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp39-cp39-musllinux_1_2_i686.whl |
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| Size | 171.7 kB |
| Tags | CPython 3.9 Linux musl 1.2+ x86-32 |
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SHA-256 checksum How to use checksums |
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No |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp39-cp39-manylinux_2_17_x86_64.manylinux2014_x86_64.whl |
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| Size | 168.0 kB |
| Tags | CPython 3.9 Linux glibc 2.17+ x86-64 |
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SHA-256 checksum How to use checksums |
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No |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp39-cp39-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp39-cp39-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl |
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| Size | 170.4 kB |
| Tags | CPython 3.9 Linux glibc 2.17+ x86-32 Linux glibc 2.5+ x86-32 |
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No |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp39-cp39-macosx_11_0_arm64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp39-cp39-macosx_11_0_arm64.whl |
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| Size | 136.0 kB |
| Tags | CPython 3.9 macOS 11.0+ ARM64 |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp38-cp38-win_amd64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp38-cp38-win_amd64.whl |
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| Size | 130.8 kB |
| Tags | CPython 3.8 Windows x86-64 |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp38-cp38-musllinux_1_2_x86_64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp38-cp38-musllinux_1_2_x86_64.whl |
|---|---|
| Size | 170.8 kB |
| Tags | CPython 3.8 Linux musl 1.2+ x86-64 |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp38-cp38-musllinux_1_2_i686.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp38-cp38-musllinux_1_2_i686.whl |
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| Size | 170.6 kB |
| Tags | CPython 3.8 Linux musl 1.2+ x86-32 |
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SHA-256 checksum How to use checksums |
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No |
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twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp38-cp38-manylinux_2_17_x86_64.manylinux2014_x86_64.whl |
|---|---|
| Size | 167.2 kB |
| Tags | CPython 3.8 Linux glibc 2.17+ x86-64 |
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| Uploaded via |
twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp38-cp38-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp38-cp38-manylinux_2_5_i686.manylinux1_i686.manylinux_2_17_i686.manylinux2014_i686.whl |
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| Size | 168.8 kB |
| Tags | CPython 3.8 Linux glibc 2.17+ x86-32 Linux glibc 2.5+ x86-32 |
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No |
| Uploaded via |
twine/6.1.0 CPython/3.12.3
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Release files / networkx_algo_common_subtree-0.2.2-cp38-cp38-macosx_11_0_arm64.whl
| Download URL | networkx_algo_common_subtree-0.2.2-cp38-cp38-macosx_11_0_arm64.whl |
|---|---|
| Size | 136.3 kB |
| Tags | CPython 3.8 macOS 11.0+ ARM64 |
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SHA-256 checksum How to use checksums |
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No |
| Uploaded via |
twine/6.1.0 CPython/3.12.3
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