Social network analysis with NetworkX

Introduction

In this tutorial, we will show you how to perform a simple network analysis with the NetworkX library and data stored in Memgraph. You will also acquire a basic understanding of query modules, an easy method for extending the query language with user-written procedures.

To get started, please install Memgraph using the memgraph-platform image by following the installment instructions for your OS.

Once Memgraph is up and running, there are three ways to execute queries and procedures in Memgraph:

• using Memgraph Lab, a visual user interface that you can use from your browser at http://localhost:3000 or download as an application
• using the command-line tool mgconsole
• using drivers and the Bolt protocol

For this tutorial, you are going to need Memgraph Lab to import the dataset and then you can query it either with Memgraph Lab or with mgconsole. We used the results from the command-line tool mgconsole because of the format.

Data model

We are going to use the Karate Club graph, a network of friendships between 34 members of a karate club at a US university, as described by Wayne Zachary in 1977. It is a very popular data set in social network analysis and is very often referenced in such tutorials. The nodes in the graph represent the members while the relationships between them are of type FRIENDS_WITH. You can differentiate the nodes by using their unique id property.

Import the dataset

To import the dataset, open Memgraph Lab and navigate to the Datasets tab in the sidebar. From there, load the Karate club friendship network dataset, wait for the import to finish, move to the Query tab or mgconsole and continue with the tutorial.

Use existing NetworkX algorithms

Execute the following command to get all the relationships inside our network:

MATCH (s)-[r]-(t)
RETURN s, r, t;

Now we have a better overview of what we are dealing with, so it’s time to get some useful information about the network.

To analyze the network we will use the built-in procedure analyze() from the graph_analyzer query module. This module utilizes the NetworkX library to retrieve graph information. Run the following query:

CALL graph_analyzer.analyze() YIELD *;

You will get details about the graph, such as the number of nodes, edges, bridges and many more.

Betweenness centrality

Now let's try to find the betweenness centrality of a node, i.e. the number of times a node acts as a bridge along the shortest path between two other nodes. Run the following query:

CALL nxalg.betweenness_centrality() YIELD *;

The procedure betweenness_centrality() is one of over 70 algorithms available in the nxalg module.

The result should be:

+--------------+--------------+
| betweenness  | node         |
+--------------+--------------+
| 0            | ({id: "0"})  |
| 0.000473485  | ({id: "1"})  |
| 0.0083649    | ({id: "2"})  |
| 0.00189394   | ({id: "3"})  |
| 0            | ({id: "4"})  |
| 0.000473485  | ({id: "5"})  |
| ...          | ...          |

Link prediction

A very common problem in network analysis is link prediction. The algorithm predicts which new interactions among the network members are likely to occur in the near future. One way of predicting these links is by measuring the “proximity” of nodes in a network. This can be done by using the Jaccard coefficient. Let's try running the algorithm on a node with the id 13 and ordering the results descending by the value of the coefficient:

CALL nxalg.jaccard_coefficient()
YIELD *
WITH  u, v, coef
WHERE u.id = '13'
RETURN u, v, coef
ORDER BY coef DESC;

The results are:

+--------------+--------------+--------------+
| u            | v            | coef         |
+--------------+--------------+--------------+
| ({id: "13"}) | ({id: "19"}) | 0.6          |
| ({id: "13"}) | ({id: "17"}) | 0.4          |
| ({id: "13"}) | ({id: "21"}) | 0.4          |
| ({id: "13"}) | ({id: "28"}) | 0.333333     |
| ({id: "13"}) | ({id: "30"}) | 0.285714     |
| ({id: "13"}) | ({id: "27"}) | 0.285714     |
| ({id: "13"}) | ({id: "31"}) | 0.222222     |
| ({id: "13"}) | ({id: "15"}) | 0.166667     |
| ({id: "13"}) | ({id: "14"}) | 0.166667     |
| ({id: "13"}) | ({id: "18"}) | 0.166667     |
| ({id: "13"}) | ({id: "20"}) | 0.166667     |
| ({id: "13"}) | ({id: "22"}) | 0.166667     |
| ({id: "13"}) | ({id: "26"}) | 0.166667     |
| ({id: "13"}) | ({id: "32"}) | 0.133333     |
| ({id: "13"}) | ({id: "29"}) | 0.125        |
| ({id: "13"}) | ({id: "23"}) | 0.111111     |
| ({id: "13"}) | ({id: "25"}) | 0            |
| ({id: "13"}) | ({id: "24"}) | 0            |
| ({id: "13"}) | ({id: "16"}) | 0            |
+--------------+--------------+--------------+

Add new NetworkX algorithms as query modules

Memgraph comes with over 70 NetworkX algorithms, but if the algorithm you require is missing, you can add it yourself as a query module.

Let's create a custom module, add it to the /usr/lib/memgraph/query_modules directory within Docker then load it into Memgraph to query the data.

Community detection algorithm

Detecting communities in a network is a very common problem. Therefore, we need community detection algorithms that can partition the network into multiple communities. Let's create our own module that accomplishes this task. Create a file called communities.py on your computer and copy the following code into it:

import mgp
import networkx as nx
from networkx.algorithms import community
from mgp_networkx import MemgraphDiGraph


@mgp.read_proc
def detect(
    ctx: mgp.ProcCtx
    ) -> mgp.Record(communities=mgp.List[mgp.List[mgp.Vertex]]):

    networkxGraph = nx.DiGraph(MemgraphDiGraph(ctx=ctx))
    communities_generator = community.girvan_newman(networkxGraph)

    return mgp.Record(communities=[
        list(s) for s in next(communities_generator)])

We just created a query module with the procedure detect() that utilizes the Girvan–Newman method to find communities in a graph.

Copy the module into Docker

1. Open a new terminal and find out the CONTAINER ID of the memgraph-platform container by running:

   docker ps

2. Position yourself in the directory where communities.py is located and copy the file to the memgraph-platform container by running:

   docker cp communities.py CONTAINER_ID:/usr/lib/memgraph/query_modules/movielens2.py

   Be sure to replace the CONTAINER_ID.

3. Check if you copied the file correctly! Enter the container:

   docker exec -it CONTAINER_ID bash

4. List all the files in the /usr/lib/memgraph/query_modules folder and check if the communities.py file is there:

   ls /usr/lib/memgraph/query_modules

Load a new query module into Docker

Once your query module is safe in Docker, you can load it into Memgraph.

All modules are automatically loaded into Memgraph when it starts, but if the module was copied into Docker while Memgraph was already running, like it was now, it needs to be loaded by using a Cypher procedure.

You can either use the CALL mg.load_all() procedure to reload all existing modules and load any newly added ones,
or CALL mg.load("module_name") to (re)load a specific module.

CALL mg.load_all();

Call a query module

Let's call the custom query module with Cypher:

CALL communities.detect()
YIELD communities
UNWIND communities AS community
RETURN community;

The resulting communities are:

+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| community                                                                                                                                                                                                                                                               |
+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| [({id: "0"}), ({id: "1"}), ({id: "3"}), ({id: "4"}), ({id: "5"}), ({id: "6"}), ({id: "7"}), ({id: "10"}), ({id: "11"}), ({id: "12"}), ({id: "13"}), ({id: "16"}), ({id: "17"}), ({id: "19"}), ({id: "21"})]                                                             |
| [({id: "2"}), ({id: "8"}), ({id: "9"}), ({id: "14"}), ({id: "15"}), ({id: "18"}), ({id: "20"}), ({id: "22"}), ({id: "23"}), ({id: "24"}), ({id: "25"}), ({id: "26"}), ({id: "27"}), ({id: "28"}), ({id: "29"}), ({id: "30"}), ({id: "31"}), ({id: "32"}), ({id: "33"})] |
+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+

Further reading

If you want to find out more about query modules, take a look at our guide on how to create your own: Implement custom query modules.

You can also visit our NetworkX Reference guide to find out which NetworkX algorithms are already available in Memgraph.