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Concept module

Graph Representation and Adjacency Intuition

Keep one live graph, one local neighborhood, and one frontier cue visible together so graph structure feels readable before traversal rules get formal.

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Featured setups

Layered campus from A

Open a graph where the first neighborhood is small and easy to read.

Hub and detours from C

Start from the hub so one node fans out into two detours immediately.

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Starter track

Step 3 of 60 / 6 complete

Algorithms and Search Foundations

Earlier steps still set up Graph Representation and Adjacency Intuition.

1. Sorting and Algorithmic Trade-offs2. Binary Search / Halving the Search Space3. Graph Representation and Adjacency Intuition4. Breadth-First Search and Layered Frontiers+2 more steps

Previous step: Binary Search / Halving the Search Space.

Start from track beginning

Why it behaves this way

Explanation

A graph should feel like a live neighborhood map, not an abstract list of circles and lines. This bench keeps one labeled graph, one active frontier, and one adjacency readout together so local connections stay readable before the search language gets more formal.

Adjacency is the first honest question: which nodes can the current node touch directly right now? Once that local neighborhood is visible, breadth-first and depth-first search become different ways of organizing the same next-step options.

Key ideas

01A graph is built from nodes and edges, but the useful reading is local adjacency.
02The frontier is just the set of adjacent next candidates that have already been claimed but not fully explored.
03Changing the start node changes the first neighborhood even when the graph itself stays the same.

Frozen walkthrough

Step through the frozen example

Frozen walkthrough
Read one neighborhood directly from the bench before you talk about algorithms.

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Frozen valuesUsing frozen parameters

On the layered campus graph, what does the start node A make visible immediately?

Graph layout

Layered campus

Start node

A

First frontier

B, C

1. Read only the direct neighbors first

Node A touches B and C directly, so those two nodes are the first adjacent candidates.

2. Turn that neighborhood into a frontier

After the first expansion, the claimed next-step frontier is [B, C] rather than the whole graph.

3. Name what stays the same later

Breadth-first and depth-first search will organize that frontier differently, but they still start from the same local adjacency picture.

First neighborhood read

From A, the first frontier is B and C.
Adjacency is the local structure that every later search rule has to respect.

Common misconception

Reading a graph means looking at the whole diagram at once and guessing a path globally.

The honest first move is local: read the neighbors of the current node.

Search grows from one neighborhood to the next, not from a magical full-map scan.

Mini challenge

Move the start node until the first neighborhood clearly widens.

Make a prediction before you reveal the next step.

Decide whether you need a hub node or an edge node before you move the slider.

Check your reasoning against the live bench.

Start from a hub node if you want the first frontier to widen immediately.
A hub has more adjacent neighbors, so the frontier fans out sooner even though the graph is the same object.

Quick test

Reasoning

Question 1 of 2

Answer from the visible neighborhood, not from memorized graph jargon.

What does adjacency mean on this graph bench?

Use the live bench to test the result before moving on.

Accessibility

The simulation shows one labeled graph with the current node, the frontier nodes, and the visited nodes colored differently so local neighborhoods stay visible.

A readout card reports the traversal mode, the current node, the frontier size, and the target, while a cue panel shows the frontier order and the current neighbor list.

Graph summary

One graph tracks visited nodes against frontier size, a second tracks the current depth against the deepest claimed depth, and a third compares new discoveries with repeat skips.

The graph hover and the step-through-time rail stay tied to the same live traversal bench.