DSA Graphs — Fundamentals Visualized

Learn graph fundamentals — vertices, edges, directed vs undirected, weighted graphs, interactive visualizer, and real-world network examples.

Jul 4, 20264 min read

Introduction

Graphs model relationships — unlike trees (one parent per node), graphs allow arbitrary connections, cycles, and multiple paths between vertices.

Social networks, road maps, dependency graphs, and the web are all graphs.

Quick index

#	Section
1	How graphs work
2	Interactive visualizer
3	Full implementation
4	Graph types
5	vs trees
6	Real-life examples

1. How graphs work

plaintext

A graph G = (V, E) has a set of vertices V and edges E connecting them.

Term	Meaning
Vertex (node)	An entity — user, city, web page
Edge (link)	A connection between two vertices
Degree	Number of edges touching a vertex
Path	Sequence of edges connecting two vertices
Cycle	Path that starts and ends at the same vertex

Back to index

2. Interactive visualizer

Graphs — Fundamentals

Vertices and edges model networks — social graphs, maps, dependencies, and the web.

A graph G = (V, E) — vertices (nodes) connected by edges (links).

Graph basics

// V = { A, B, C, D, E, F }
// E = { A-B, A-C, B-D, B-E, C-F }

const graph = {
  A: ["B", "C"],
  B: ["A", "D", "E"],
  C: ["A", "F"],
  // ...
}

Unlike trees, graphs can have cycles and multiple paths between nodes.

Vertices

Edges

Space

O(V+E)

Back to index

3. Full implementation

class Graph {
  constructor(directed = false) {
    this.adj = new Map()
    this.directed = directed
  }
 
  addVertex(v) {
    if (!this.adj.has(v)) this.adj.set(v, [])
  }
 
  addEdge(a, b, weight = 1) {
    this.addVertex(a)
    this.addVertex(b)
    this.adj.get(a).push({ to: b, weight })
    if (!this.directed) this.adj.get(b).push({ to: a, weight })
  }
 
  getNeighbors(v) {
    return this.adj.get(v) ?? []
  }
 
  hasEdge(a, b) {
    return this.getNeighbors(a).some((e) => e.to === b)
  }
 
  degree(v) {
    return this.getNeighbors(v).length
  }
 
  vertexCount() {
    return this.adj.size
  }
}
 
function buildSampleGraph() {
  const g = new Graph(false)
  ;['A', 'B', 'C', 'D', 'E', 'F'].forEach((v) => g.addVertex(v))
  g.addEdge('A', 'B')
  g.addEdge('A', 'C')
  g.addEdge('B', 'D')
  g.addEdge('B', 'E')
  g.addEdge('C', 'F')
  return g
}

Function calls with output

// ── Demo calls — output shown on the right ──
const g = buildSampleGraph()
 
g.vertexCount() // → 6
g.getNeighbors('A') // → [{ to:'B', weight:1 }, { to:'C', weight:1 }]
g.degree('B') // → 3
g.hasEdge('A', 'C') // → true
g.hasEdge('D', 'F') // → false

Back to index

4. Graph types

Type	Edges	Example
Undirected	Two-way	Facebook friends
Directed	One-way	Twitter follows
Weighted	Cost on edge	GPS distance
Unweighted	All equal	Web page links
Cyclic	Has a cycle	Circular dependency
Acyclic (DAG)	No cycles	Build pipeline

Back to index

5. vs trees

Structure	Connections	Cycles	Root
Tree	Parent → children	No	Yes (single)
Graph	Any vertex to any	Yes	No

Back to index

6. Real-life examples

Scenario	Graph role
Social network	Users = vertices, friendships = edges
Google Maps	Intersections = vertices, roads = weighted edges
npm dependencies	Packages = vertices, requires = directed edges
Web crawling	Pages = vertices, hyperlinks = directed edges

Social network friend graph

Users are vertices, friendships are edges — mutual connections form an undirected graph.

Aliceid:1[0]

Bobid:2[1]

Each user becomes a vertex in the graph.

Real-world implementation

class SocialGraph {
  constructor() { this.adj = new Map() }
  addUser(id) { if (!this.adj.has(id)) this.adj.set(id, new Set()) }
  addFriendship(a, b) {
    this.addUser(a); this.addUser(b)
    this.adj.get(a).add(b)
    this.adj.get(b).add(a)
  }
  friendsOf(id) { return [...(this.adj.get(id) ?? [])] }
  mutualFriends(a, b) {
    const fa = this.adj.get(a) ?? new Set()
    return [...(this.adj.get(b) ?? [])].filter(f => fa.has(f))
  }
}

Full working code for the scenario above.

Function calls with output

// ── Function calls with output ──
const net = new SocialGraph()
net.addUser("Alice"); net.addUser("Bob")	→ 2 vertices

Side output shows return value after each call — step through to trace execution.

Back to index

Summary

Graphs model arbitrary relationships — vertices and edges with optional direction and weight. Next: how to store them efficiently.

Next reads: Graphs Implementation · Graph Traversal

Share this article

X LinkedIn Facebook

Subscribe to my newsletter

Stay up to date and get notified when I share new contents.

No spam ever, unsubscribe anytime

Back to Blog

DSA Graphs Data Structures

DSA Graphs — Fundamentals Visualized

Learn graph fundamentals — vertices, edges, directed vs undirected, weighted graphs, interactive visualizer, and real-world network examples.

Jul 4, 20264 min read

Introduction

Graphs model relationships — unlike trees (one parent per node), graphs allow arbitrary connections, cycles, and multiple paths between vertices.

Social networks, road maps, dependency graphs, and the web are all graphs.

Quick index

#	Section
1	How graphs work
2	Interactive visualizer
3	Full implementation
4	Graph types
5	vs trees
6	Real-life examples

1. How graphs work

plaintext

A graph G = (V, E) has a set of vertices V and edges E connecting them.

Term	Meaning
Vertex (node)	An entity — user, city, web page
Edge (link)	A connection between two vertices
Degree	Number of edges touching a vertex
Path	Sequence of edges connecting two vertices
Cycle	Path that starts and ends at the same vertex

Back to index

2. Interactive visualizer

Graphs — Fundamentals

Vertices and edges model networks — social graphs, maps, dependencies, and the web.

A graph G = (V, E) — vertices (nodes) connected by edges (links).

Graph basics

// V = { A, B, C, D, E, F }
// E = { A-B, A-C, B-D, B-E, C-F }

const graph = {
  A: ["B", "C"],
  B: ["A", "D", "E"],
  C: ["A", "F"],
  // ...
}

Unlike trees, graphs can have cycles and multiple paths between nodes.

Vertices

Edges

Space

O(V+E)

Back to index

3. Full implementation

class Graph {
  constructor(directed = false) {
    this.adj = new Map()
    this.directed = directed
  }
 
  addVertex(v) {
    if (!this.adj.has(v)) this.adj.set(v, [])
  }
 
  addEdge(a, b, weight = 1) {
    this.addVertex(a)
    this.addVertex(b)
    this.adj.get(a).push({ to: b, weight })
    if (!this.directed) this.adj.get(b).push({ to: a, weight })
  }
 
  getNeighbors(v) {
    return this.adj.get(v) ?? []
  }
 
  hasEdge(a, b) {
    return this.getNeighbors(a).some((e) => e.to === b)
  }
 
  degree(v) {
    return this.getNeighbors(v).length
  }
 
  vertexCount() {
    return this.adj.size
  }
}
 
function buildSampleGraph() {
  const g = new Graph(false)
  ;['A', 'B', 'C', 'D', 'E', 'F'].forEach((v) => g.addVertex(v))
  g.addEdge('A', 'B')
  g.addEdge('A', 'C')
  g.addEdge('B', 'D')
  g.addEdge('B', 'E')
  g.addEdge('C', 'F')
  return g
}

Function calls with output

// ── Demo calls — output shown on the right ──
const g = buildSampleGraph()
 
g.vertexCount() // → 6
g.getNeighbors('A') // → [{ to:'B', weight:1 }, { to:'C', weight:1 }]
g.degree('B') // → 3
g.hasEdge('A', 'C') // → true
g.hasEdge('D', 'F') // → false

Back to index

4. Graph types

Type	Edges	Example
Undirected	Two-way	Facebook friends
Directed	One-way	Twitter follows
Weighted	Cost on edge	GPS distance
Unweighted	All equal	Web page links
Cyclic	Has a cycle	Circular dependency
Acyclic (DAG)	No cycles	Build pipeline

Back to index

5. vs trees

Structure	Connections	Cycles	Root
Tree	Parent → children	No	Yes (single)
Graph	Any vertex to any	Yes	No

Back to index

6. Real-life examples

Scenario	Graph role
Social network	Users = vertices, friendships = edges
Google Maps	Intersections = vertices, roads = weighted edges
npm dependencies	Packages = vertices, requires = directed edges
Web crawling	Pages = vertices, hyperlinks = directed edges

Social network friend graph

Users are vertices, friendships are edges — mutual connections form an undirected graph.

Aliceid:1[0]

Bobid:2[1]

Each user becomes a vertex in the graph.

Real-world implementation

class SocialGraph {
  constructor() { this.adj = new Map() }
  addUser(id) { if (!this.adj.has(id)) this.adj.set(id, new Set()) }
  addFriendship(a, b) {
    this.addUser(a); this.addUser(b)
    this.adj.get(a).add(b)
    this.adj.get(b).add(a)
  }
  friendsOf(id) { return [...(this.adj.get(id) ?? [])] }
  mutualFriends(a, b) {
    const fa = this.adj.get(a) ?? new Set()
    return [...(this.adj.get(b) ?? [])].filter(f => fa.has(f))
  }
}

Full working code for the scenario above.

Function calls with output

// ── Function calls with output ──
const net = new SocialGraph()
net.addUser("Alice"); net.addUser("Bob")	→ 2 vertices

Side output shows return value after each call — step through to trace execution.

Back to index

Summary

Graphs model arbitrary relationships — vertices and edges with optional direction and weight. Next: how to store them efficiently.