Introduction
This blog covers the culminating project of our five-week workshop on Graph Convolutional Networks, a niche within graph-based machine learning.
We began with Graph Neural Networks (GNNs) fundamentals, leveraging tools like the Neo4j graph database and Python. This equipped me with the skills to construct and analyze graph data efficiently.
Moreover, the curriculum included topics on topological link prediction and creating a recommendation system.
Below, I detail the process of establishing a graph-based database using Neo4j and Cypher Queries, followed by the application of predictive algorithms like Adamic Adar, Common Neighbors, Preferential Attachment, Resource Allocation, Same Community, Total Neighbors, to forecast relationships, and how to compile the outcomes into a CSV file.
Creating Graph Database in Neo4j
// Person nodes
CREATE (alice:Person {name: 'Alice', gender: 'Female', age: 30, bornIn: 'New York'}),
(bob:Person {name: 'Bob', gender: 'Male', age: 32, bornIn: 'London'}),
(carol:Person {name: 'Carol', gender: 'Female', age: 25, bornIn: 'Sydney'}),
(dave:Person {name: 'Dave', gender: 'Male', age: 28, bornIn: 'Toronto'}),
(eve:Person {name: 'Eve', gender: 'Female', age: 22, bornIn: 'Paris'}),
(frank:Person {name: 'Frank', gender: 'Male', age: 35, bornIn: 'Berlin'}),
(grace:Person {name: 'Grace', gender: 'Female', age: 29, bornIn: 'Tokyo'}),
(hank:Person {name: 'Hank', gender: 'Male', age: 40, bornIn: 'Cape Town'}),
(irene:Person {name: 'Irene', gender: 'Female', age: 24, bornIn: 'Moscow'}),
(jack:Person {name: 'Jack', gender: 'Male', age: 27, bornIn: 'Rio de Janeiro'})
// Pets
CREATE (rocky:Pet {name: 'Rocky', species: 'Dog', breed: 'Golden Retriever'}),
(bella:Pet {name: 'Bella', species: 'Cat', breed: 'Siamese'}),
(max:Pet {name: 'Max', species: 'Parrot', breed: 'Macaw'}),
(lucy:Pet {name: 'Lucy', species: 'Rabbit', breed: 'Holland Lop'})
// Products
CREATE (smartphone:Product {name: 'Smartphone', brand: 'TechBrand'}),
(laptop:Product {name: 'Laptop', brand: 'CompTech'}),
(book:Product {name: 'Book', title: 'The Great Adventure'})
// Activities
CREATE (jogging:Activity {name: 'Jogging', fact: 'Can increase lifespan by 3 years'}),
(painting:Activity {name: 'Painting', fact: 'Improves mental health and creativity'}),
(cooking:Activity {name: 'Cooking', fact: 'Is a form of therapeutic art'})
// relationships
CREATE (alice)-[:MARRIED_TO {MarriedOn: '2020-02-25'}]->(bob),
(bob)-[:DIVORCED_FROM {DivorcedOn: '2023-09-02'}]->(alice),
(carol)-[:SURPRISED]->(dave),
(eve)-[:OWNS]->(rocky),
(frank)-[:OWNS]->(bella),
(grace)-[:OWNS]->(max),
(hank)-[:OWNS]->(lucy),
(irene)-[:FRIENDS_WITH {since: '2021-09-19'}]->(jack),
(jack)-[:MARRIED_TO]->(irene),
(alice)-[:BOUGHT]->(smartphone),
(bob)-[:BOUGHT]->(laptop),
(carol)-[:READS]->(book),
(dave)-[:PARTICIPATES_IN]->(jogging),
(eve)-[:PRACTICES]->(painting),
(frank)-[:ENJOYS]->(cooking),
(grace)-[:USES]->(smartphone),
(hank)-[:WORKS_ON]->(laptop),
(irene)-[:STUDIES]->(book),
(jack)-[:EXERCISES_WITH]->(jogging),
(max)-[:CARED_FOR_BY]->(grace),
(lucy)-[:PLAYS_WITH]->(jack),
(laptop)-[:NEEDED_FOR]->(cooking),
(jogging)-[:LIKED_BY]->(hank),
(painting)-[:CHOSEN_BY]->(carol),
(cooking)-[:LEARNED_BY]->(alice),
(hank)-[:FRIENDS_WITH]->(jack)
RETURN *Creating Person Nodes
I start by creating several person nodes, each defined with attributes such as name, gender, age, and place of birth. These nodes represent individuals like Alice, Bob, Carol, and others.
Adding Pet Nodes
Next, I define pet nodes with details such as name, species, and breed, including pets like Rocky (a dog), Bella (a cat), and others.
Listing Product Nodes
I also create product nodes to represent items like a Smartphone, Laptop, and a Book, each with specific characteristics like brand or title.
Establishing Activity Nodes
I then introduce activity nodes representing various activities, such as Jogging, Painting, and Cooking, with attributes highlighting certain facts about each activity.
Forming Relationships
Afterward, I establish relationships between these nodes with specific types and properties. For example:
- I connect Alice and Bob through marital and later divorce relationships.
- I illustrate ownership relationships between people and pets (e.g., Eve owns Rocky).
- I detail friendships, work relations, and recreational activities (e.g., Irene is friends with Jack, Hank works on a laptop, and Frank enjoys cooking).
- I link people to products or activities (e.g., Alice bought a smartphone, Carol reads a book, and Dave participates in jogging).
These relationships often come with additional properties, like dates for marriages or friendships, showing not just the type of relationship but also the important details of that relationship.
Visualizing the Graph
Finally, I use “match (n) return n” command to display all the nodes I’ve created and their relationships, effectively visualizing the entire graph I’ve constructed through the above commands.
This process helps me build a rich, interconnected graph that models complex relationships between people, their interests, possessions, and activities, demonstrating the capabilities of graph databases in representing and querying relational data from my perspective.
This is the result:
Topological link prediction algorithms:
The Adamic Adar algorithm was introduced in 2003 by Lada Adamic and Eytan Adar to predict links in a social network. It is computed using the following formula:
where N(u) is the set of nodes adjacent to u.
A value of 0 indicates that two nodes are not close, while higher values indicate nodes are closer.
The library contains a function to calculate the closeness between two nodes.
Common neighbors capture the idea that two strangers who have a friend in common are more likely to be introduced than those who don’t have any friends in common.
It is computed using the following formula:
where N(x) is the set of nodes adjacent to the node x, and N(y) is the set of nodes adjacent to the node y.
A value of 0 indicates that two nodes are not close, while higher values indicate nodes are closer.
The library contains a function to calculate the closeness between two nodes.
Preferential Attachment is a measure used to compute the closeness of nodes, based on their shared neighbors.
Preferential attachment means that the more connected a node is, the more likely it is to receive new links. This algorithm was popularised by Albert-László Barabási and Réka Albert through their work on scale-free networks. It is computed using the following formula:
where N(u) is the set of nodes adjacent to u.
A value of 0 indicates that two nodes are not close, while higher values indicate that nodes are closer.
The library contains a function to calculate the closeness between two nodes.
Resource Allocation is a measure used to compute the closeness of nodes based on their shared neighbors.
The Resource Allocation algorithm was introduced in 2009 by Tao Zhou, Linyuan Lü, and Yi-Cheng Zhang as part of a study to predict links in various networks. It is computed using the following formula:
where N(u) is the set of nodes adjacent to u.
A value of 0 indicates that two nodes are not close, while higher values indicate nodes are closer.
The library contains a function to calculate the closeness between two nodes.
Same Community is a way of determining whether two nodes belong to the same community. These communities could be computed by using one of the Community detection.
If two nodes belong to the same community, there is a greater likelihood that there will be a relationship between them in future, if there isn’t already.
A value of 0 indicates that two nodes are not in the same community. A value of 1 indicates that two nodes are in the same community.
The library contains a function to calculate closeness between two nodes.
Total Neighbors computes the closeness of nodes, based on the number of unique neighbors that they have. It is based on the idea that the more connected a node is, the more likely it is to receive new links.
Total Neighbors is computed using the following formula:
where N(x) is the set of nodes adjacent to x, and N(y) is the set of nodes adjacent to y.
A value of 0 indicates that two nodes are not close, while higher values indicate nodes are closer.
The library contains a function to calculate the closeness between two nodes.
Let’s Run all link prediction algorithms in one Query:
MATCH (p1:Person {name: 'Hank'}), (p2:Person {name: 'Jack'})
WITH p1, p2
RETURN
gds.alpha.linkprediction.adamicAdar(p1, p2) AS AdamicAdar,
gds.alpha.linkprediction.commonNeighbors(p1, p2) AS CommonNeighbors,
gds.alpha.linkprediction.preferentialAttachment(p1, p2) AS PreferentialAttachment,
gds.alpha.linkprediction.resourceAllocation(p1, p2) AS ResourceAllocation,
gds.alpha.linkprediction.sameCommunity(p1, p2) AS SameCommunity,
gds.alpha.linkprediction.totalNeighbors(p1, p2) AS TotalNeighborsResult:
Thank you for taking the time to read this article; your valuable feedback is warmly welcomed.
Furthermore, I would be happy to assist you in solving a puzzle during your data journey.
pouya [at] sattari [dot] org
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