Directed vs undirected graphs in Data Structures Theory - Visual Side-by-Side Comparison

Concept Flow - Directed vs undirected graphs

Start with nodes

↓

Add edges

↓

Directed: edges have direction

↓

Edge from A to B only

↓

Undirected: edges no direction

↓

Edge between A and B both ways

Graphs start with nodes, then edges are added. Edges can be directed (one-way) or undirected (two-way).

Execution Sample

Data Structures Theory

Nodes = {A, B}
Edges Directed = {(A->B)}
Edges Undirected = {(A-B)}

Shows two nodes with one directed edge from A to B and one undirected edge between A and B.

Analysis Table

Step	Operation	Graph Type	Edge Added	Effect on Connections	Visual State
1	Create nodes A and B	Directed & Undirected	None	Nodes A, B exist	Nodes: A, B; No edges
2	Add edge A->B	Directed	A->B	Connection from A to B only	A -> B
3	Add edge A-B	Undirected	A-B	Connection both ways between A and B	A <-> B
4	Check edge B->A in Directed	Directed	None	No edge from B to A	A -> B
5	Check edge B->A in Undirected	Undirected	None	Edge exists from B to A (same as A to B)	A <-> B

💡 All nodes and edges added; differences in directionality shown

State Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	After Step 5
Nodes	{}	{A, B}	{A, B}	{A, B}	{A, B}	{A, B}
Directed Edges	{}	{}	{(A->B)}	{(A->B)}	{(A->B)}	{(A->B)}
Undirected Edges	{}	{}	{}	{(A-B)}	{(A-B)}	{(A-B)}

Key Insights - 3 Insights

Why does the directed graph only show connection from A to B but not from B to A?

Because directed edges have a direction, so an edge A->B means only from A to B. Step 4 in execution_table shows no edge B->A.

Why does the undirected graph show connection both ways between A and B?

Undirected edges have no direction, so edge A-B means connection both ways. Step 5 in execution_table confirms B to A connection exists.

Are nodes affected differently in directed vs undirected graphs?

No, nodes remain the same; only edges differ in directionality as shown in variable_tracker and execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at Step 2. What edge is added in the directed graph?

A Edge from B to A

B Edge from A to B

C Edge between A and B with no direction

D No edge added

💡 Hint

Check the 'Edge Added' column at Step 2 in execution_table

At which step does the undirected graph show a two-way connection between nodes?

A Step 2

B Step 4

C Step 3

D Step 5

💡 Hint

Look at the 'Effect on Connections' column for undirected graph edges

If we add an edge B->A in the directed graph, how would the variable 'Directed Edges' change after Step 4?

A It would include {(A->B), (B->A)}

B It would remain {(A->B)}

C It would become empty

D It would include {(A-B)}

💡 Hint

Consider how directed edges store direction; see variable_tracker for Directed Edges

Concept Snapshot

Graphs have nodes connected by edges.
Directed graphs have edges with direction (A->B).
Undirected graphs have edges without direction (A-B).
Directed edges connect one way; undirected connect both ways.
Nodes stay the same; edges define connection type.
Understanding edge direction is key to graph behavior.

Full Transcript

This visual execution trace shows the difference between directed and undirected graphs. We start by creating two nodes, A and B. Then, we add a directed edge from A to B, which means the connection goes only one way. Next, we add an undirected edge between A and B, which connects both nodes in both directions. The execution table tracks each step, showing how edges affect connections. The variable tracker records the state of nodes and edges after each step. Key moments clarify common confusions about edge direction and node roles. The quiz tests understanding by referencing specific steps and variable states. Overall, directed graphs have one-way edges, while undirected graphs have two-way edges, affecting how nodes connect.