Social Network Analysis

My capstone project for the Object Oriented Java Programming: Data Structures and Beyond Specialization, offered by University of California San Diego ( UCSD ).

This project investigates the communities within a social network. The first part of the project will look at relationships between a user’s friends (specifically, are they all connected as friends too). In the second part, the goal will be to find the minimum dominating set, so we can reach all the people in the network just sharing with a number of friends.

Small Test Case

for visualization JUNG library is needed

Data

facebook_ucsd.txt This graph contains Facebook friendships between students at UCSD in 2005. This data was originally stored in a Matlab sparse matrix; however, this was processed using Python to create a more suitable format for reading with Java. The edges in this file are directed; however, each edge also appears in reverse order, making the final result undirected.

Source: https://archive.org/details/oxford-2005-facebook-matrix

Citation: Facebook data scrape related to paper "The Social Structure of Facebook Networks", by Amanda L. Traud, Peter J. Mucha, Mason A. Porter.

• Number of nodes (users) = 14947

Questions

Easier: For a given user, which of their friends aren’t connected as friends? For example, if the given user, Maria, is friends with both Jamaal and Huang, if Jamaal and Huang are not friends, we’ll suggest them as potential friends.

Harder: Find the Exact Cover Set. Figure out the smallest set of people who are connected to everyone in the network. For example, if everyone in the smallest set were to post something to their friends, everyone would see the post.

Algorithms, Data Structures, and Answer to Question

Main Data Structure: The network has been laid out as a classic graph using an adjacency list. Each individual in the graph is a vertex and an edge between vertices represents a friendship. This should work for both problems. Each node is stored as the key in a HashMap, with values representing the node’s outgoing edges, stored as a HashSet for quick O(1) lookup.

The exact cover problem is represented in Algorithm X using a matrix A consisting of 0s and 1s. The goal is to select a subset of the rows so that the digit 1 appears in each column exactly once.

Algorithm X functions as follows:

If the matrix A has no columns, the current partial solution

is a valid solution; terminate successfully. 

Otherwise, choose a column c (deterministically). 

Choose a row r such that A[r] = 1 (nondeterministically). 

Include row r in the partial solution. 

For each column j such that A[r][j] = 1,

    for each row i such that A[i][j] = 1, 
    
        delete row i from matrix A. 
        
    delete column j from matrix A. 
  
Repeat this algorithm recursively on the reduced matrix A. 

Test Results

//facebook_1000 -> 214
//facebook_2000 -> 223
//facebook_ucsd -> 357 (16K Nodes)