Graph Terminology Vertices Edges Directed Undirected Weighted in DSA C - Execution Trace

Concept Flow - Graph Terminology Vertices Edges Directed Undirected Weighted

Start: Define Graph

↓

Identify Vertices (Nodes)

↓

Identify Edges (Connections)

↓

Check Edge Type

↓

Directed

↓

Check Weight

↓

Weighted

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Graph Fully Defined

This flow shows how a graph is built by defining vertices, edges, then classifying edges as directed or undirected, and weighted or unweighted.

Execution Sample

DSA C

Graph G = {
  Vertices: {A, B, C},
  Edges: {(A->B, 5), (B->C, 3)}
};

Defines a graph with 3 vertices and 2 directed weighted edges.

Execution Table

Step	Operation	Vertices	Edges	Edge Type	Weight	Visual State
1	Initialize graph	{}	{}	N/A	N/A	Graph is empty
2	Add vertex A	{A}	{}	N/A	N/A	A
3	Add vertex B	{A, B}	{}	N/A	N/A	A B
4	Add vertex C	{A, B, C}	{}	N/A	N/A	A B C
5	Add edge A->B with weight 5	{A, B, C}	{(A->B)}	Directed	5	A --5--> B C
6	Add edge B->C with weight 3	{A, B, C}	{(A->B), (B->C)}	Directed	3	A --5--> B --3--> C
7	Check if edges are weighted	{A, B, C}	{(A->B), (B->C)}	Directed	Weighted	Edges have weights 5 and 3
8	Graph fully defined	{A, B, C}	{(A->B), (B->C)}	Directed	Weighted	Final graph with 3 vertices and 2 weighted directed edges

💡 All vertices and edges added; graph classification complete.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	After Step 6	Final
Vertices	{}	{A}	{A, B}	{A, B, C}	{A, B, C}	{A, B, C}	{A, B, C}
Edges	{}	{}	{}	{}	{(A->B)}	{(A->B), (B->C)}	{(A->B), (B->C)}
Edge Type	N/A	N/A	N/A	N/A	Directed	Directed	Directed
Weight	N/A	N/A	N/A	N/A	5 (A->B)	3 (B->C)	Weighted

Key Moments - 3 Insights

Why do we say edges can be directed or undirected?

Because edges show connections between vertices; directed edges have a direction (like one-way street), undirected edges do not (like two-way street). See execution_table steps 5 and 6 where edges are added as directed.

What does it mean for edges to be weighted?

Weighted edges have numbers (weights) showing cost or distance. In the table steps 5 and 6, weights 5 and 3 are assigned to edges, meaning these connections have values.

Can a graph have vertices without edges?

Yes, vertices can exist alone without edges. In step 4, vertices A, B, C exist before edges are added in step 5.

Visual Quiz - 3 Questions

Look at the execution_table at step 5, what is the edge type added?

A Undirected

B Directed

C Weighted

D Unweighted

💡 Hint

Check the 'Edge Type' column at step 5 in execution_table.

At which step are all vertices added to the graph?

A Step 4

B Step 3

C Step 2

D Step 6

💡 Hint

Look at the 'Vertices' column in execution_table to see when {A, B, C} appear.

If edges were unweighted, how would the 'Weight' column change at step 6?

A It would show weights as 0

B It would show the same weights

C It would show 'N/A' or no weights

D It would show negative weights

💡 Hint

Refer to the 'Weight' column in execution_table and think about what unweighted means.

Concept Snapshot

Graph = set of vertices (nodes) and edges (connections).
Edges can be directed (one-way) or undirected (two-way).
Edges can be weighted (have values) or unweighted.
Vertices can exist without edges.
Graph types depend on edge direction and weights.

Full Transcript

A graph is made of vertices and edges. Vertices are points or nodes. Edges connect vertices. Edges can have direction: directed edges go one way, undirected edges go both ways. Edges can also have weights, which are numbers showing cost or distance. Vertices can exist alone without edges. This example shows adding vertices A, B, C, then adding directed weighted edges A to B with weight 5, and B to C with weight 3. The graph is then fully defined as directed and weighted.