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

Concept Flow - Graph Terminology Vertices Edges Directed Undirected Weighted

Start: Define Graph

↓

Vertices: Points/Nodes

↓

Edges: Connections

↓

Directed?

Yes→Edges have direction

↓

Undirected: Edges bidirectional

↓

Weighted?

Yes→Edges have weights (costs)

No↓

Edges unweighted

This flow shows how a graph is built from vertices and edges, then edges can be directed or undirected, and weighted or unweighted.

Execution Sample

DSA Typescript

const vertices = ['A', 'B', 'C'];
const edges = [
  { from: 'A', to: 'B', weight: 5 },
  { from: 'B', to: 'C', weight: 3 }
];

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

Execution Table

Step	Operation	Vertices	Edges	Edge Type	Weighted	Visual State
1	Initialize vertices	['A', 'B', 'C']	[]	N/A	N/A	Vertices: A, B, C; No edges yet
2	Add edge from A to B with weight 5	['A', 'B', 'C']	[A -> B (5)]	Directed	Yes	A --5--> B; C isolated
3	Add edge from B to C with weight 3	['A', 'B', 'C']	[A -> B (5), B -> C (3)]	Directed	Yes	A --5--> B --3--> C
4	Check if edges are directed	['A', 'B', 'C']	[A -> B (5), B -> C (3)]	Directed	Yes	Edges have direction from source to target
5	Check if edges are weighted	['A', 'B', 'C']	[A -> B (5), B -> C (3)]	Directed	Yes	Edges carry weights 5 and 3
6	End of graph definition	['A', 'B', 'C']	[A -> B (5), B -> C (3)]	Directed	Yes	Graph fully defined

💡 All vertices and edges added; graph is directed and weighted

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
vertices	[]	['A', 'B', 'C']	['A', 'B', 'C']	['A', 'B', 'C']
edges	[]	[A -> B (5)]	[A -> B (5), B -> C (3)]	[A -> B (5), B -> C (3)]
edgeType	N/A	Directed	Directed	Directed
weighted	N/A	Yes	Yes	Yes

Key Moments - 3 Insights

Why do we say edges are 'directed' or 'undirected'?

Because directed edges have a clear start and end point (like one-way streets), while undirected edges connect two vertices both ways (like two-way streets). See execution_table rows 2 and 4 where edges are added and identified as directed.

What does it mean for edges to be weighted?

Weighted edges carry a number (weight) that can represent cost, distance, or capacity. In the table rows 2 and 3, each edge has a weight (5 and 3), showing weighted edges.

Can a graph have both directed and undirected edges?

Usually a graph is either directed or undirected for consistency. Mixing them is possible but uncommon and complicates traversal. Our example in rows 4 and 5 shows a directed graph.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, how many edges does the graph have?

A 1

B 3

C 2

D 0

💡 Hint

Check the 'Edges' column at step 3 in execution_table

At which step do we confirm the edges are weighted?

A Step 2

B Step 5

C Step 4

D Step 6

💡 Hint

Look at the 'Weighted' column in execution_table rows

If edges were undirected, how would the visual state change at step 3?

A Edges would have arrows both ways between vertices

B Edges would disappear

C Vertices would be removed

D Weights would be ignored

💡 Hint

Refer to concept_flow where directed edges have one arrow, undirected have two-way connection

Concept Snapshot

Graph = vertices (points) + edges (connections)
Edges can be directed (one-way) or undirected (two-way)
Edges can be weighted (carry a number) or unweighted
Directed edges show direction from source to target
Weighted edges represent cost, distance, or capacity

Full Transcript

A graph consists of vertices, which are points or nodes, and edges, which connect these vertices. Edges can be directed, meaning they go from one vertex to another in a specific direction, or undirected, meaning the connection goes both ways. Additionally, edges can be weighted, carrying a number that represents cost or distance, or unweighted, meaning no such number is attached. In the example, we defined three vertices A, B, and C, and added two directed weighted edges: from A to B with weight 5, and from B to C with weight 3. This setup helps understand basic graph terminology and structure.