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Merge pull request #267 from Mec-iS/issue-261-graph-algebra
Starting graph algebra
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Diff for: ‎examples/graph_algebra/gla_ex0_0.ipynb

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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Graph Algebra with `kglab`\n",
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"\n",
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"## intro\n",
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"`kglab` provides tools to access graph data from multiple source to build a `KnowledgeGraph` that can be easily used by data scientists. For a thorough explanation of how to use triples-stored data and how to load this data into `kglab` please see examples in the `examples/` directory. The examples in this directory (`examples/graph_algebra/`) will care to introduce graph algebra capabilities to be used on the graphs the user has loaded. \n",
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"\n",
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"## basic load and querying\n",
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"In particular, once your data is loaded in a `KnowledgeGraph` with something like:\n",
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"\n",
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"1. Instantiate a graph from a dataset:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<kglab.kglab.KnowledgeGraph at 0x7f283f3d3940>"
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]
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},
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"execution_count": 1,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"# for use in tutorial and development; do not include this `sys.path` change in production:\n",
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"import sys ; sys.path.insert(0, \"../../\")\n",
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"from os.path import dirname\n",
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"import kglab\n",
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"import os\n",
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"\n",
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"namespaces = {\n",
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" \"foaf\": \"http://xmlns.com/foaf/0.1/\",\n",
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" \"gorm\": \"http://example.org/sagas#\",\n",
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" \"rel\": \"http://purl.org/vocab/relationship/\",\n",
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" }\n",
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"\n",
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"kg = kglab.KnowledgeGraph(\n",
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" name = \"Happy Vikings KG example for SKOS/OWL inference\",\n",
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" namespaces=namespaces,\n",
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" )\n",
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"\n",
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"kg.load_rdf(dirname(dirname(os.getcwd())) + \"/dat/gorm.ttl\")"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"2. It is possible to create a subgraph by providing a SPARQL query, by defining a \"subject\" and \"object\":\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"metadata": {},
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"outputs": [],
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"source": [
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"query = \"\"\"SELECT ?subject ?object\n",
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"WHERE {\n",
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" ?subject rdf:type gorm:Viking .\n",
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" ?subject gorm:childOf ?object .\n",
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"}\n",
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"\"\"\""
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n",
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"## define a subgraph\n",
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"In this case we are looking for the network of parent-child relations among members of Vikings family.\n",
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"\n",
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"With this query we can define a **subgraph** so to have access to **graph algebra** capabilities: "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [],
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"source": [
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"from kglab.subg import SubgraphMatrix\n",
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"\n",
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"subgraph = SubgraphMatrix(kg=kg, sparql=query)\n"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## compute Adjacency matrices\n",
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"Let's compute the first basic adjacency matrix (usually noted with `A`):"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0., 1., 1., 0., 0.],\n",
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" [0., 0., 0., 1., 0.],\n",
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" [0., 0., 0., 0., 0.],\n",
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" [0., 0., 0., 0., 1.],\n",
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" [0., 0., 0., 0., 0.]])"
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]
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},
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"execution_count": 4,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"adj_matrix = subgraph.to_adjacency()\n",
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"adj_matrix"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"what happened here is that all the subjects and objects have been turned into integer indices from 0 to number of nodes. So we can see that the entity with index 0 is adjancent (is connected, has a directed edge) to the entity with index 1. This is a directed graph because the relationship `gorm:childOf` goes from child to parent, let's turn this into an undirected graph so to see the relation in a more symmetric way (both the child-parent and parent-child)."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([[0., 1., 1., 0., 0.],\n",
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" [1., 0., 0., 1., 0.],\n",
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" [1., 0., 0., 0., 0.],\n",
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" [0., 1., 0., 0., 1.],\n",
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" [0., 0., 0., 1., 0.]])"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"undirected_adj_mtx = subgraph.to_undirected()\n",
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"undirected_adj_mtx"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"We can see now the relationship is a generic symmetric \"parenthood\" relations, not just a child-parent directed relationship."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3.8.10 64-bit ('.venv': venv)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.10"
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},
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"orig_nbformat": 4,
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"vscode": {
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"interpreter": {
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"hash": "de68f9b565e1e230f4433adb1a318d8f3a0dfad0917fa0c696727472c8ddadbf"
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}
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}

Diff for: ‎kglab/algebra.py

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"""
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Working with `SubgraphMatrix` as vectorized representation.
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Additions to functionalities present in `subg.py`.
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Integrate `scipy` and `scikit-learn` functionalities.
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see license https://github.com/DerwenAI/kglab#license-and-copyright
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"""
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import typing
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import networkx as nx
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from networkx import DiGraph
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class AlgebraMixin:
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"""
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Provides methods to work with graph algebra using `SubgraphMatrix` data.
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NOTE: provide optional Oxigraph support for fast in-memory computation
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"""
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nx_graph: typing.Optional[DiGraph] = None
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def to_undirected(self):
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return nx.to_numpy_array(self.nx_graph.to_undirected())
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def to_adjacency(self):
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"""
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Return adjacency (dense) matrix for the KG.
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[Relevant NetworkX interface](https://networkx.org/documentation/stable/reference/convert.html#id2)
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returns:
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`numpy.array`: the array representation in `numpy` standard
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"""
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self.check_attributes()
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return nx.to_numpy_array(self.nx_graph)
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def to_incidence(self):
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"""
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Return incidence (dense) matrix for the KG.
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[Relevant scipy docs](https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.csr_matrix.html)
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returns:
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`numpy.array`: the array representation in `numpy` standard
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"""
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self.check_attributes()
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return nx.incidence_matrix(self.nx_graph).toarray()
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def to_laplacian(self):
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"""
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Return Laplacian matrix for the KG. Graph is turned into undirected.
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[docs](https://networkx.org/documentation/stable/reference/generated/networkx.linalg.laplacianmatrix.laplacian_matrix.html)
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returns:
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`numpy.array`: the array representation in `numpy` standard
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"""
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self.check_attributes()
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return nx.laplacian_matrix(self.nx_graph.to_undirected()).toarray()
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def to_scipy_sparse(self):
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"""
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Return graph in CSR format (optimized for matrix-matrix operations).
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returns:
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SciPy sparse matrix: Graph adjacency matrix.
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"""
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self.check_attributes()
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return nx.to_scipy_sparse_array(self.nx_graph)

Diff for: ‎kglab/networks.py

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"""
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Working with `SubgraphMatrix` as vectorized representation.
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Additions to functionalities present in `subg.py`.
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Integrate `scikit-network` functionalities.
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see license https://github.com/DerwenAI/kglab#license-and-copyright
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"""
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import sknetwork as skn
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class NetAnalysisMixin:
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"""
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Provides methods for network analysis tools to work with `KnowledgeGraph`.
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"""
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def get_distances(self, adj_mtx):
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"""
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Compute distances according to an adjacency matrix.
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"""
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self.check_attributes()
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return skn.path.get_distances(adj_mtx)
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def get_shortest_path(self, adj_matx, src, dst):
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"""
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Return shortest path from sources to destinations according to an djacency matrix.
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adj_mtx:
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numpy.array: adjacency matrix for the graph.
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src:
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int or iterable: indices of source nodes
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dst:
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int or iterable: indices of destination nodes
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returns:
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list of int: a path of indices
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"""
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self.check_attributes()
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return skn.path.get_shortest_path(adj_matx, src, dst)
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# number of nodes, number of edges
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# density
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# triangles
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# reciprocity

Diff for: ‎kglab/query/mixin.py

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pythonify: bool = True,
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) -> pd.DataFrame:
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"""
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Wrapper for [`rdflib.Graph.query()`](https://rdflib.readthedocs.io/en/stable/apidocs/rdflib.html?highlight=query#rdflib.Graph.query) to perform a SPARQL query on the RDF graph.
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Wrapper for [`rdflib.Graph.query()`](https://rdflib.readthedocs.io/en/stable/apidocs/rdflib.html?highlight=query#rdflib.Graph.query)
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to perform a SPARQL query on the RDF graph.
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sparql:
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text for the SPARQL query
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notebook: bool = False,
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) -> pyvis.network.Network:
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"""
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Visualize the given SPARQL query as a [`pyvis.network.Network`](https://pyvis.readthedocs.io/en/latest/documentation.html#pyvis.network.Network)
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Visualize the given SPARQL query as a
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[`pyvis.network.Network`](https://pyvis.readthedocs.io/en/latest/documentation.html#pyvis.network.Network)
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sparql:
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input SPARQL query to be visualized
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pythonify: bool = True,
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) -> typing.Any:
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"""
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Wrapper for RDFlib [`n3()`](https://rdflib.readthedocs.io/en/stable/utilities.html?highlight=n3#serializing-a-single-term-to-n3) and [`toPython()`](https://rdflib.readthedocs.io/en/stable/apidocs/rdflib.html?highlight=toPython#rdflib.Variable.toPython) to serialize a node into a human-readable representation using N3 format.
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Wrapper for RDFlib [`n3()`](https://rdflib.readthedocs.io/en/stable/utilities.html?highlight=n3#serializing-a-single-term-to-n3)
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and [`toPython()`](https://rdflib.readthedocs.io/en/stable/apidocs/rdflib.html?highlight=toPython#rdflib.Variable.toPython)
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to serialize a node into a human-readable representation using N3 format.
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node:
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must be a [`rdflib.term.Node`](https://rdflib.readthedocs.io/en/stable/apidocs/rdflib.html?highlight=Node#rdflib.term.Node)

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