Scott

Scott is a software able to compute, for any labelled (edge and node) graph, a canonical tree representative of its isomorphism class, that we can derive to a canonical trace (string) or adjacency matrix.

Table of contents

This repository summary aims to be synthetic and straight to the goal. For more informations about the graph isomorphism problem, algorithm details, please refer to the repo page.

• Getting started
  • From source code
  • From Pypi
  • From Docker
• Usage
  • Import Graphs
  • Canonical traces
  • Canonical Adjacency Matrices
• Citation
• Licence
• References

Getting started

From source code

Simply clone the repo in a local repertory

# get the code
git clone https://github.com/theplatypus/scott.git
cd ./scott

# (optionnal) install using setuptools
python3 setup.py install

Then you should be able to import scott package from python :

import scott as st

From Pypi

pip install <todo>

From Docker

To get scott in an environment with additional dependencies installed (chemical librabries, jupyter notebooks,etc.), a Docker container is available :

# Build the image containing all the stuff for a simple standalone install
docker build -t scott .
# or pull it
docker pull docker.pkg.github.com/theplatypus/scott/scott:latest

# run an interactive shell, where you can import scott in python default interpreter
docker run --rm -it scott

# or run a jupyter notebook including scott
docker run -it -p 8888:8888 scott /bin/bash -c "jupyter notebook --notebook-dir=/opt/notebooks --ip='*' --port=8888 --no-browser --allow-root"

For specific uses, you have access to alternative Dockerfiles in /dockerfiles, each of them being a tag that you can also pull.

Pypy

An image including the Pypy interpreter, a high-performance alternative to the classic CPython. Use it with ipython or launch a jupyter server.

docker build -t scott:pypy -f dockerfiles/pypy/Dockerfile .
docker run -it --rm -p 8888:8888 scott:pypy

# > ipython 
# > jupyter notebook --notebook-dir=/opt/notebooks --ip='*' --port=8888 --no-browser --allow-root

Debian

A debian-based image, if you are not an Anaconda supporter.

docker build -t scott:debian -f dockerfiles/debian/Dockerfile .
docker run -it --rm -p 8888:8888 scott:debian

# > ipython 
# > jupyter notebook --notebook-dir=/opt/notebooks --ip='*' --port=8888 --no-browser --allow-root

PySpark

An image designed to run inside a Spark cluster.

docker build -t scott:spark -f dockerfiles/pyspark/Dockerfile .

docker run -it -v $(pwd):/home/scott scott:spark pyspark --master local[*]

---

Usage

For more informations about code usage, please refer to usage.py and usage_advanced.py.

Build a Graph

You can describe a Graph algorithmically.

import scott as st

# describe a graph from scratch

graph = st.structs.graph.Graph()
n1 = st.structs.node.Node("1", "C")
n2 = st.structs.node.Node("2", "O")
n3 = st.structs.node.Node("3", "H")	
n4 = st.structs.node.Node("4", "H")

e1 = st.structs.edge.Edge("1", n1, n2, modality=2)
e2 = st.structs.edge.Edge("2", n1, n3)
e3 = st.structs.edge.Edge("3", n1, n4)

graph.add_node(n1)
graph.add_nodes([n2, n3, n4])
graph.add_edge(e1)
graph.add_edge(e2)
graph.add_edge(e3)

print(n1)
print(e1)
print(graph)

Import Graphs

Scott is also able to parse a few graph formats files. Note that a parsing function always returns a list, even if there is one molecule in the file.

# Parse a .sdf file (chemical file standard) :

# from blob...
CAFEINE_URL = "https://drive.google.com/uc?id=1lXeFVGS77oK_qL3NESDV_UjJknPyiICx"
file_content = urlopen(CAFEINE_URL).read().decode()

compounds = st.parse.from_sdf(file_content, ignore_hydrogens = False)
cafeine = compounds[0]
print(cafeine)

# ... or from file path - note we ignore hydrogens this time
compounds = st.parse.from_sdf(file_path='./data/molecule/cafeine.sdf', ignore_hydrogens = True)
cafeine_without_H = compounds[0]
print(cafeine_without_H)

# Parse a SMILES string (RDKit required)
smile = st.parse.parse_smiles('CCOCOCC=CCONC')

# we can iterate over graph vertices
for id_node in smile.V :
	print("Node #%s : %s" % (str(id_node), str(smile.V[id_node].label)))

# Parse a .dot file
cfi1 = st.parse.from_dot(file_path = './data/isotest/cfi-rigid-t2-dot/cfi-rigid-t2-0016-04-1.dot')[0]

# Parse a .dimacs file
cfi2 = st.parse.from_dimacs(file_path = './data/isotest/cfi-rigid-t2/cfi-rigid-t2-0016-04-1')[0]

Canonical traces

A canonical trace is a string representation of the tree representative of an isomorphism class. This is the main feature of Scott.

simple = st.parse.from_pubchem_xml(file_path= './data/molecule/simple.xml')[0]

# we get a CGraph object from the function `st.canonize.to_cgraph`...
simple_cgraph = st.canonize.to_cgraph(simple)

# ...that we can print directly or convert to string
simple_canon = str(simple_cgraph)

assert simple_canon == '(H:1, H:1, (H:1, H:1, ((((C:1).#2{$1}:2)C:2)C:2, ((((C:1).#2{$1}:2)C:2)C:1).#2{$2}:1)C:1)C:1, (O:2, (((((C:1).#2{$1}:2)C:2)C:1).#2{$2}:1)O:1)C:1)C'

If you only need a hash function for graphs, you can apply a string hash function (md5, sha, etc.) to the trace obtained.

import hashlib 

assert hashlib.sha224(simple_canon.encode()).hexdigest() == 'a90f308ea4c2cd8a1003a32507b4769f5ef5f31bb4f2602856200982'

G = st.parse.from_dimacs(file_path = './data/isotest/cfi-rigid-t2/cfi-rigid-t2-0020-01-1')[0]
H = st.parse.from_dimacs(file_path = './data/isotest/cfi-rigid-t2/cfi-rigid-t2-0020-01-2')[0]

E = st.parse.from_dimacs(file_path = './data/isotest/cfi-rigid-t2/cfi-rigid-t2-0020-02-2')[0]
F = st.parse.from_dimacs(file_path = './data/isotest/cfi-rigid-t2/cfi-rigid-t2-0020-02-2')[0]

# Can take few seconds
Gc = st.canonize.to_cgraph(G)
Hc = st.canonize.to_cgraph(H)
Ec = st.canonize.to_cgraph(E)
Fc = st.canonize.to_cgraph(F)

# So, following the nomenclature G == H and E == F, ...

assert str(Gc) == str(Hc)
assert str(Ec) == str(Fc)

# ... but G != E/F and H != E/F 
assert str(Gc) != str(Ec)
assert str(Hc) != str(Fc)

Canonical Adjacency Matrices

On a graph G of N vertices, an adjacency matrix A is a N*N array describing the link between two vertices. Scott can help to get a standardized adjacency matrix, such as isomophic graph will have the exact same adjacency matrices, which can help learning process by bringing the "same elements towards the same neurons".

# Let g and h be two isomorphic graphs
g = st.parse.from_dot(file_path="./data/isotest/cfi-rigid-t2-dot/cfi-rigid-t2-0020-02-2.dot")[0]
h = st.parse.from_dot(file_path="./data/isotest/cfi-rigid-t2-dot/cfi-rigid-t2-0020-02-1.dot")[0]

# if we compare their adjacency matrix, it is very unlikely to get the two exact same matrices,
# as there is no order on vertices
g.adjacency_matrix() == h.adjacency_matrix()
# False

# but if we induce an order based on the representant tree given by scott,
# there is only one canonical adjacecny matrix
assert g.adjacency_matrix(canonic = True) == h.adjacency_matrix(canonic = True)

Citation

If you use or fork scott in further works, please cite the following :

@inproceedings{bloyet2019scott,
  title={Scott: A method for representing graphs as rooted trees for graph canonization},
  author={Bloyet, Nicolas and Marteau, Pierre-Fran{\c{c}}ois and Frenod, Emmanuel},
  booktitle={International Conference on Complex Networks and Their Applications},
  pages={578--590},
  year={2019},
  organization={Springer}
}

Licence

The Python source code we provide is available on the GitHub repo, under the MIT public licence.

Feel free to improve it.

Written and developed by :

• Nicolas BLOYET (See-d, IRISA Expression, LMBA)
• Pierre-François MARTEAU (IRISA Expression)
• Emmanuel FRÉNOD (See-d, LMBA)