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What is a graph?

A graph has vertices and edges.

What is a graph?

A graph is a data structure of vertices and edges connecting them. Unlike a tree it can contain cycles.

In a directed graph edges have a direction (A→B); in an undirected one they are bidirectional (A—B). In a weighted graph edges have a cost.

Graphs are used in pathfinding, social networks, dependency resolution.

Directed and undirected

In a directed graph each edge has a direction: A→B means from A to B but not B to A. In an undirected graph A—B can be traversed both ways.

In the adjacency list a directed graph has graph[A] containing only B; an undirected one has both graph[A] and graph[B] containing each other.

Direction is achieved by adding to both sides during insertion.

Practice Create graph

Write create_graph(). Return an empty adjacency dict. Print {} with print(create_graph()).

Starter code

solution.py
def create_graph():
    # Empty graph

Sample solution

solution.py
def create_graph():
    # Empty graph
    return {}
print(create_graph())

Expected output

{}

Questions and answers

Review the lesson questions together with their answers. To test yourself, solve the lesson interactively.

1 How does a graph differ from a tree?

  • No vertices
  • It can contain cycles Correct answer
  • No edges
  • Has a root

Explanation: It can contain cycles

2 Edge direction

Question 
Undirected graph A—B: add B to graph[A] and add A to graph[____]
Answer 
Undirected graph A—B: add B to graph[A] and add A to graph[A]

Explanation: A is right.

3 What is a graph: match the terms

Term Meaning
Directed One way
Undirected Both ways
Weighted Cost
Cycle Allowed

All lessons in Intermediate

1 Merge sort

  1. Divide and conquer
  2. Merge operation
  3. Full merge sort
  4. Summary - Merge sort

2 Quick sort

  1. Pivot selection
  2. Partitioning
  3. Recursive quick sort
  4. Summary - Quick sort

3 Heap sort

  1. What is a heap?
  2. Heapify
  3. Build heap and sort
  4. Summary - Heap sort

4 Counting sort

  1. Counting idea
  2. Count array
  3. Output array
  4. Summary - Counting sort

5 Radix sort

  1. Radix idea
  2. Digit pass
  3. Stable sub-sort
  4. Summary - Radix sort

6 Sorting project

  1. Project: Overview
  2. Score array
  3. Apply merge sort
  4. Print statistics

7 Tree

  1. What is a tree?
  2. Node and edge
  3. Binary tree
  4. Summary - Trees

8 Binary search tree

  1. BST rule
  2. BST insert
  3. BST search
  4. Summary - BST

9 AVL tree

  1. Balanced tree
  2. Rotation
  3. Balance after insert
  4. Summary - AVL tree

10 Heap

  1. Min and max heap
  2. Insert
  3. Extract
  4. Summary - Heap

11 Priority queue

  1. What is a priority queue?
  2. Heap-based implementation
  3. Push and pop
  4. Summary - Priority queue

12 Data structures project

  1. Project: Overview
  2. Undo stack
  3. Pending queue
  4. Print the state

13 Graph basics

  1. What is a graph?
  2. Adjacency list
  3. Adjacency matrix
  4. Summary - Graph

14 Breadth-first search

  1. BFS idea
  2. Using a queue
  3. Marking visited
  4. Summary - BFS

15 Depth-first search

  1. DFS idea
  2. Stack or recursion
  3. Backtracking
  4. Summary - DFS

16 Greedy algorithms

  1. Greedy approach
  2. Coin change
  3. Greedy limits
  4. Summary - Greedy

17 Divide and conquer

  1. Three steps
  2. Recursive structure
  3. Master theorem
  4. Summary - Divide and conquer

18 Backtracking

  1. What is backtracking?
  2. State tree
  3. Pruning
  4. Summary - Backtracking

19 Graph project

  1. Project: Overview
  2. City graph
  3. BFS for reachability
  4. Print the result

20 Intermediate final

  1. Challenge 1
  2. Challenge 2
  3. Challenge 3
  4. Challenge 4