Assignment 1: Random Graphs and Network Models

Overview

This assignment explores fundamental concepts in network science, including small-world phenomena, scale-free networks, and phase transitions in random graphs. You will implement various network models and analyze their structural properties through both theoretical derivations and computational simulations.

Submission Guidelines

File Format

• Submit a single ZIP file named: SN_HW1_[StudentNumber].zip
• Contents must include:
  • Report in PDF format
  • All code files (Python/MATLAB/etc.)
• Upload to the eLearn platform

Questions & Support

• Contact TAs via email only (avoid social media DMs)
• TAs: Faezeh Mozaffari, Farzad Jannati

AI Tool Usage

• You must document any use of AI tools (ChatGPT, Copilot, etc.)
• Include in your report:
  • Which tools you used
  • How you used them
  • Link to ChatGPT conversations (if applicable)

Late Policy

• Up to 7 days late accepted with 5% penalty per day
• After 7 days: No submissions accepted

Academic Integrity

• Plagiarism = -0.25 grade for ALL involved students
• Random verification sessions (5-10 minutes) will be conducted
• Discrepancies between report and presentation increase re-selection probability

Grading Criteria

• Theoretical Questions (30%)
  • Mathematical rigor and clarity
  • Correct derivations with explanations
• Implementation & Code (40%)
  • Correct algorithm implementation
  • Code quality and documentation
  • Reproducibility
• Analysis & Insights (30%)
  • Quality of visualizations
  • Depth of analysis
  • Comparison with theory
  • AI tool documentation

Required Libraries (Suggested)

# Python
import networkx as nx
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.stats import linregress