Advanced & Applied Topics · Network Analysis & Graph Theory

Network and graph analysis: Substructures and community detection

Public introduction · full guide in Eikos

Introduction

What this guide covers

Introduction Chart from the original guide

Overview

Topics covered

  • Introduction
  • Network Analysis: Substructures and Communities
  • Mathematical Foundations of Graph Theory and Complex Networks
  • The Laplacian Matrix and its Variants
  • Global Structural Measures
  • Reference Network Models (Null Models)

Related concepts

Main connections

  • Linear algebra & matrices
  • Calculus & differentiation
  • Mean & expected value
  • Unsupervised learning & clustering
  • Supervised machine learning
  • Markov chain Monte Carlo (MCMC)

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

Aij={w(vi,vj)if (vi,vj)∈E0In another case
View LaTeX sourceA_{ij} = \begin{cases} w(v_i, v_j) & \text{if } (v_i, v_j) \in E \\ 0 & \text{In another case} \end{cases}