OrbitSI using NetworkX for Python

OrbitSI is a NetworkX-based Python package that efficiently solves the subgraph isomorphism enumeration problem, i.e., finding all subgraphs in a large data graph G_d that are isomorphic to a pattern/query graph G_p. It also supports fast vertex orbit counting, which summarises the local structural roles of vertices within a network.

OrbitSI combines orbit-based filtering and ordering to prune and order candidate node mappings, significantly reducing the search space during subgraph matching. It integrates two state-of-the-art orbit counting engines — EVOKE and ORCA — via optimised C++ bindings using pybind11, and builds the search pipeline using networkx.

The package includes a command-line interface (CLI), usable library, and testing utilities. It is installable via pip, tested on synthetic and real-world benchmark datasets, and fully open source under the Apache 2.0 license.

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Wiki

• Introduction
• Subgraph Isomorphism
• Orbit Counting

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Installation

Install from PyPi:

pip install orbitsi

Install from source

1. Clone the repository:

git clone https://hpdc-gitlab.eeecs.qub.ac.uk/sitauhidi/orbitsi-nx.git
cd orbitsi-nx

2. Build and install:

pip install .

Requires Python 3.8+, NumPy, NetworkX, and a C++17 compiler (e.g., g++ or clang++).

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Command-Line Interface (CLI) Usage

Once installed, the orbitsi CLI tool allows you to perform:

1. Subgraph Isomorphism Search
2. Node Orbit Counting

To confirm installation:

orbitsi --help

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Subgraph Isomorphism Search

Find all subgraphs in a large graph G_d that are isomorphic to a smaller query/pattern graph G_p.

Command:

orbitsi search --data <path_to_data_graph> --pattern <path_to_pattern_graph> [--orbit-counter evoke|orca] [--graphlet-size 4|5]

Arguments:

• --data: Path to the data graph file (required)
• --pattern: Path to the pattern/query graph file (required)
• --orbit-counter: Orbit counting backend, either evoke (default) or orca
• --graphlet-size: Graphlet size to use for orbit counting (4 or 5, default: 4)

Example:

orbitsi search --data datasets/data_graph/HPRD.graph --pattern datasets/query_graph/query1.graph --orbit-counter evoke --graphlet-size 4

Orbit Counting for a Graph

Compute node orbit vectors for a given graph using either the EVOKE or ORCA backend.

Command:

orbitsi count-orbits --graph <path_to_graph> [--orbit-counter evoke|orca] [--graphlet-size 4|5] [--induced]

Arguments:

• --graph: Path to the graph file (required)
• --orbit-counter: Orbit counting backend, either evoke (default) or orca
• --graphlet-size: Size of graphlets to consider (4 or 5)
• --induced: Flag to compute induced orbit counts (optional; default is non-induced)

Example:

orbitsi count-orbits --graph datasets/data_graph/HPRD.graph --orbit-counter orca --graphlet-size 5 --induced

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Graph File Format

All graphs should be in .graph format:

t N M
v 0 1 2
v 1 2 1
...
e 0 1
e 1 2
...

• t N M: number of nodes N and edges M
• v ID Label Degree: vertex ID, label (label is required), degree (optional)
• e u v: edge between vertex u and v

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Testing

A complete suite of unit and integration tests is provided in the tests/ directory. This includes:

• Benchmark-based validation for subgraph isomorphism
• Cross-validation of orbit counting with external tools

To get started, see tests/README.md for detailed setup and usage instructions.

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Citation

If you use OrbitSI for subgraph isomorphism search, please cite:

Tauhidi, Syed Ibtisam, Arindam Karmakar, Thai Son Mai, and Hans Vandierendonck. "OrbitSI: An Orbit-based Algorithm for the Subgraph Isomorphism Search Problem." In 2024 IEEE International Conference on Knowledge Graph (ICKG), pp. 360-369. IEEE, 2024. https://doi.org/10.1109/ICKG63256.2024.00052

If you only use the orbit counting modules (ORCAOrbitCounter, EVOKEOrbitCounter), cite:

• EVOKE: Noujan Pashanasangi and C. Seshadhri. "Efficiently counting vertex orbits of all 5-vertex subgraphs, by EVOKE.", WSDM 2020: Proceedings of the 13th International Conference on Web Search and Data Mining, pp. 447–455. https://doi.org/10.1145/3336191.3371773

• ORCA: Tomaž Hočevar and Janez Demšar. "A combinatorial approach to graphlet counting." Bioinformatics, 30(4): 559–565, 2014. https://doi.org/10.1093/bioinformatics/btt717

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Acknowledgement

This work was supported by:

• Kelvin Living Lab [grant number EP/Z531054/1]
• Ministry of Education, Government of India through the collaboration between Queen's University Belfast and Tezpur University.

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License

This project is licensed under the Apache License 2.0.

See the LICENSE file for details.