Graphs & representations
Define directed, undirected, weighted and simple graphs and choose representations that preserve the relation of interest.
Side 213Side Studies / Research
Subject
Graph Theory
Purpose
Networks of vertices and edges studied through paths, connectivity, trees, coloring, flows and structural invariants.
Structure
05 movesFormal systemV0
Definitions → structures → relations → proof → application
Reduce relational structure to graphs without losing the question.
Graph theory provides a formal toolkit for connectivity and constraint problems while separating abstract graph properties from the domain that produced the network.
Paths & connectivity
Study reachability, components, cycles and cuts as structural properties governing movement and separation.
Trees & spanning structure
Use acyclic connected graphs to represent hierarchy and minimal connective structure.
Coloring, matching & flows
Model allocation, conflict and transport constraints through reusable graph optimization problems.
Spectral & structural invariants
Use matrices, degree patterns and other invariants to connect local structure with global graph behavior.
Keep the boundaries visible.
graph ≠ network data set
tree ≠ hierarchy in every sense
shortest path ≠ best route
Questions that organize the Side.
Which graph representation preserves the mechanism being studied?
How do local degree patterns constrain global connectivity?
When does an optimization problem on a graph become computationally hard?
What should carry weight here?
Proofs concern abstract graphs; applications need a separate justification that the real-world relation is encoded faithfully.