Graph Terminology Vertices Edges Directed Undirected Weighted in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a vertex in a graph?

A vertex (or node) is a fundamental unit in a graph that represents an entity or point. It can connect to other vertices through edges.

beginner

Define an edge in graph terminology.

An edge is a connection or link between two vertices in a graph. It can be directed or undirected.

beginner

What is the difference between a directed and an undirected edge?

A directed edge has a direction from one vertex to another (like a one-way street). An undirected edge connects two vertices both ways (like a two-way street).

beginner

What does it mean if a graph is weighted?

A weighted graph has edges that carry a value or weight, representing cost, distance, or any measure between vertices.

intermediate

Can a graph have both directed and undirected edges?

Yes, such graphs are called mixed graphs, containing both directed and undirected edges.

What is a vertex in a graph?

A A point or node representing an entity

B A connection between two nodes

C A value assigned to an edge

D A path between two graphs

A vertex is a point or node in a graph representing an entity.

Which type of edge has a direction?

A Directed edge

B Weighted edge

C Undirected edge

D Loop edge

A directed edge has a direction from one vertex to another.

In an undirected graph, edges are:

A One-way connections

B Two-way connections

C Always weighted

D Not connected

Undirected edges connect vertices both ways, like two-way streets.

What does a weight on an edge represent?

A The color of the edge

B The direction of the edge

C The number of vertices

D The cost or distance between vertices

Weights represent cost, distance, or other measures on edges.

A graph with both directed and undirected edges is called:

A Simple graph

B Weighted graph

C Mixed graph

D Complete graph

A mixed graph contains both directed and undirected edges.

Explain the difference between vertices and edges in a graph.

Think of vertices as places and edges as roads connecting them.

Describe what makes a graph weighted and how weights affect edges.

Imagine roads with different lengths or toll costs.

Practice

1. In a graph, what do we call the points or nodes where edges meet?

easy

A. Paths

B. Edges

C. Weights

D. Vertices

Solution

1. Step 1: Understand graph components

   A graph consists of points called nodes and connections called edges.

2. Step 2: Identify the term for nodes

   The points or nodes where edges meet are called vertices.

3. Final Answer:

   Vertices -> Option D

4. Quick Check:

   Nodes = Vertices [OK]

Hint: Remember: nodes = vertices, connections = edges [OK]

Common Mistakes:

• Confusing edges with vertices
• Thinking weights are nodes
• Mixing paths with vertices

2. Which of the following is the correct way to declare an undirected graph using adjacency list in Go?

easy

A. graph := make(map[int][]int)

B. graph := make([][]int, 0)

C. graph := make(map[int]int)

D. graph := make([]int, 0)

Solution

1. Step 1: Understand adjacency list representation

   An adjacency list uses a map from a vertex to a list of connected vertices.

2. Step 2: Choose correct Go syntax

   Using map[int][]int creates a map from int to slice of ints, perfect for adjacency list.

3. Final Answer:

   graph := make(map[int][]int) -> Option A

4. Quick Check:

   Map of int to slice[int] = adjacency list [OK]

Hint: Adjacency list = map from node to list of nodes [OK]

Common Mistakes:

• Using map[int]int which stores single int, not list
• Using slice of slices without map for keys
• Using slice of ints which can't map nodes

3. What will be the output of the following Go code snippet representing a weighted directed graph adjacency list?

graph := map[int]map[int]int{
  1: {2: 5, 3: 10},
  2: {3: 2},
  3: {},
}
fmt.Println(graph[1][3])

medium

A. 2

B. 5

C. 10

D. 0

Solution

1. Step 1: Understand graph structure

   graph[1] is a map with keys 2 and 3, values 5 and 10 respectively.

2. Step 2: Access graph[1][3]

   graph[1][3] accesses the weight from vertex 1 to 3, which is 10.

3. Final Answer:

   10 -> Option C

4. Quick Check:

   Weight from 1 to 3 = 10 [OK]

Hint: Access nested map keys for weights: graph[from][to] [OK]

Common Mistakes:

• Confusing weight 5 (edge 1->2) with 1->3
• Assuming 0 means no edge but 3 has empty map
• Mixing up keys and values in nested maps

4. Identify the error in this Go code snippet for adding an edge to an undirected graph adjacency list:

func addEdge(graph map[int][]int, u, v int) {
  graph[u] = append(graph[u], v)
  graph[v] = append(graph[u], v)
}

medium

A. Appending v to graph[u] twice

B. Appending v to graph[v] incorrectly

C. Missing initialization of graph map

D. Using wrong data type for graph

Solution

1. Step 1: Analyze append statements

   First append adds v to graph[u], correct for edge u->v.

2. Step 2: Check second append

   Second append incorrectly appends v to graph[u] again instead of graph[v].

3. Final Answer:

   Appending v to graph[v] incorrectly -> Option B

4. Quick Check:

   Second append should be graph[v] = append(graph[v], u) [OK]

Hint: For undirected, append u to v's list and v to u's list [OK]

Common Mistakes:

• Appending to wrong slice variable
• Forgetting to append both directions
• Not initializing map slices before append

5. Given a weighted undirected graph represented as a map[int]map[int]int in Go, how can you ensure that adding an edge between two vertices u and v with weight w updates both directions correctly?

hard

A. graph[u][v] = w; graph[v][u] = w

B. graph[u][v] = w only

C. graph[v][u] = w only

D. graph[u][v] = w; graph[u][v] = w

Solution

1. Step 1: Understand undirected graph edge representation

   In undirected graphs, edges go both ways, so weights must be stored both ways.

2. Step 2: Update both directions in map

   Assign weight w to graph[u][v] and graph[v][u] to reflect undirected edge.

3. Final Answer:

   graph[u][v] = w; graph[v][u] = w -> Option A

4. Quick Check:

   Both directions updated = undirected edge [OK]

Hint: Update both graph[u][v] and graph[v][u] for undirected edges [OK]

Common Mistakes:

• Updating only one direction
• Assigning weight twice to same direction
• Confusing directed and undirected edge updates