SOLID STATE PRESS
← Back to catalog
Graph Data Structures cover
Coming soon
Coming soon to Amazon
This title is in our publishing queue.
Browse available titles
Computer Science

Graph Data Structures

Adjacency Lists, BFS/DFS, and DAGs Explained — A TLDR Primer

Graph problems show up everywhere — on AP Computer Science exams, in college data structures courses, and in nearly every technical coding interview. But most textbooks bury the core ideas under dense notation, and most tutorials assume you already know what a traversal is. If you need to get up to speed fast, this is the book.

**TLDR: Graph Data Structures** is a focused, short-by-design guide that walks you through everything you need to know before tackling shortest-path algorithms, network problems, or your next exam. Starting from scratch, it explains what vertices and edges are, how directed, weighted, and cyclic graphs differ, and when each type appears in the real world. Then it shows you the two standard ways to store a graph in code — adjacency lists and matrices — with clear tradeoff comparisons so you know which to reach for. The heart of the book is a step-by-step walkthrough of breadth-first and depth-first search, the two traversal strategies that underlie almost every other graph algorithm.

This guide is written for high school and early college students who want a computer science graphs study guide they can finish in one sitting, not a 500-page reference shelf. It's also useful for parents or tutors prepping a session on data structures. Every key term is defined in plain language, every algorithm is traced on a concrete example, and common misconceptions are called out directly.

If you have an exam, a project, or an interview coming up — pick this up and get oriented today.

What you'll learn
  • Define vertices, edges, and the main types of graphs (directed, undirected, weighted, cyclic).
  • Represent a graph in code using an adjacency list or adjacency matrix and choose between them based on tradeoffs.
  • Implement and trace breadth-first search and depth-first search on a graph.
  • Recognize real-world problems that map onto graphs and identify which graph type fits.
  • Avoid common bugs like infinite loops from unvisited tracking and confusion between trees and graphs.
What's inside
  1. 1. What Is a Graph?
    Introduces vertices and edges, contrasts graphs with trees and lists, and gives concrete examples like social networks and maps.
  2. 2. Types of Graphs: Directed, Weighted, and Cyclic
    Walks through the main flavors of graphs — directed vs undirected, weighted vs unweighted, cyclic vs acyclic, connected vs disconnected — with examples of when each shows up.
  3. 3. Representing Graphs in Code: Adjacency Lists and Matrices
    Shows the two standard ways to store a graph in memory, with code sketches and a clear comparison of time and space tradeoffs.
  4. 4. Traversing Graphs: BFS and DFS
    Introduces breadth-first and depth-first search, the visited set, and traces both algorithms step by step on a small example graph.
  5. 5. Common Graph Problems and What They Map To
    Surveys problems students will actually see — shortest path, connected components, cycle detection, topological sort — and points to which traversal or structure solves each.
Published by Solid State Press
Graph Data Structures cover
TLDR STUDY GUIDES

Graph Data Structures

Adjacency Lists, BFS/DFS, and DAGs Explained — A TLDR Primer
Solid State Press

Graph Data Structures

Adjacency Lists, BFS/DFS, and DAGs Explained — A TLDR Primer

Copyright © 2026 Solid State Press.

Published by Solid State Press.

All rights reserved. No part of this book may be reproduced or transmitted in any form without prior written permission, except for brief quotations in critical reviews and educational use.

Part of the TLDR Study Guides series.

Contents

  1. 1 What Is a Graph?
  2. 2 Types of Graphs: Directed, Weighted, and Cyclic
  3. 3 Representing Graphs in Code: Adjacency Lists and Matrices
  4. 4 Traversing Graphs: BFS and DFS
  5. 5 Common Graph Problems and What They Map To
Chapter 1

What Is a Graph?

A graph is a structure made of two things: a set of objects and a set of connections between them. That's it. The objects are called vertices (singular: vertex), and the connections are called edges. You may also hear vertex called a node — the two words mean the same thing and are used interchangeably throughout computer science.

Almost any relationship you can name fits this template. A city map: the intersections are vertices, the roads between them are edges. A social network: the people are vertices, the friendships are edges. A course catalog: the classes are vertices, the prerequisite relationships are edges. The reason graphs matter is that this simple structure — objects plus connections — turns out to describe an enormous range of real problems.

Formally, a graph $G$ is written as:

$G = (V, E)$

where $V$ is the set of vertices and $E$ is the set of edges. Each edge connects two vertices. If the graph has vertices $\{A, B, C\}$ and edges $\{(A,B),\ (B,C)\}$, then $A$ is connected to $B$, $B$ is connected to $C$, and $A$ has no direct connection to $C$. Don't be intimidated by the notation — it's just a compact way to say what the picture already shows.

Example. Draw a small graph representing three friends: Alice, Bob, and Carol. Alice and Bob know each other. Bob and Carol know each other. Alice and Carol have never met.

Solution. The vertices are $\{Alice,\ Bob,\ Carol\}$. The edges are $\{(Alice, Bob),\ (Bob, Carol)\}$. In a diagram, you'd draw three circles (one per person) and two lines — one connecting Alice–Bob and one connecting Bob–Carol. There is no line between Alice and Carol.

How a graph differs from data structures you already know

If you've studied linked lists or trees, you might wonder what makes a graph different. The distinction matters.

About This Book

If you are a high school student in an AP Computer Science course, a college freshman working through an intro data structures class, or someone grinding coding interview prep and hitting a wall on graphs, this book is for you. It is also useful for tutors who need a clean, fast reference before a session.

This computer science graphs study guide covers everything from the ground up: what vertices and edges are, how directed, weighted, and cyclic graphs differ, and how an adjacency list vs. matrix tutorial plays out in real code. It walks through BFS and DFS for beginners, covering graph traversal step by step before connecting those ideas to classic problems like cycle detection and connected components. A concise overview with no filler.

Read straight through once to build the mental map. Then work every worked example yourself before checking the solution. Finish with the practice problem set — that is where the material actually sticks.

Keep reading

You've read the first half of Chapter 1. The complete book covers 5 chapters in roughly fifteen pages — readable in one sitting.

Coming soon to Amazon