Analysis of Information Networks

Overview

This repository contains six exercises focusing on network analysis concepts and techniques. The exercises cover topics ranging from random network generation, disease modeling, and community detection to recommender systems. These tasks aim to provide hands-on experience with the analysis of different network structures, properties, and applications in real-world scenarios.

Exercises

Exercise 1: Random Network Generation and Analysis

• Task: Generate a random network of 1000 nodes with a specific edge probability and analyze its structural properties.
• Key Concepts: Erdős–Rényi model, degree distribution, clustering coefficient, shortest path length, and network diameter.
• Goal: Compare theoretical and empirical values of network properties.

Exercise 2: Calculating the Largest Component in a Random Network

• Task: Analyze the phase transition and the size of the largest component in a random network, given an average degree greater than 1.
• Key Concepts: Phase region, maximum degree, largest connected component.
• Goal: Determine the theoretical and empirical values of the network's structural properties.

Exercise 3: Degree Distribution and Assortativity in the Zachary Club Network

• Task: Analyze the Zachary Club Network by computing degree distribution, assortativity, and nearest-neighbor degree correlation.
• Key Concepts: Degree distribution, assortativity coefficient, nearest-neighbor degree correlation, eij matrix.
• Goal: Visualize the network structure and analyze the relationships between nodes and their degrees.

Exercise 4: Disease Spread

• Task: Simulate disease spread in the Zachary Club Network using the SI, SIS, and SIR models and calculate the characteristic times and epidemic thresholds.
• Key Concepts: Epidemic models (SI, SIS, SIR), characteristic time, epidemic threshold.
• Goal: Compute the epidemic thresholds and characteristic times for different models using network properties.

Exercise 5: Link Prediction

• Task: Predict the potential formation of new links in the Zachary Club Network using common neighbors, the Jaccard coefficient, and the Adamic/Adar index.
• Key Concepts: Link prediction metrics, decision tree classification.
• Goal: Implement a model to predict links and evaluate the model's accuracy.

Exercise 6: Recommender System

• Task: Analyze a rating matrix of users and items to calculate user similarity and recommend items using various distance and similarity metrics.
• Key Concepts: Jaccard distance, cosine similarity, normalization, binary rating conversion.
• Goal: Evaluate user similarity and make recommendations based on different metrics and normalization techniques.