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"∞" : v.toString() ).join(" "); console.log(`${i}: ${row}`); } } private validateVertex(v: number): void { if (v < 0 || v >= this.vertices) { throw new Error(`Vertex ${v} is out of bounds [0, ${this.vertices - 1}]`); } } }73:T899,class AdjacencyMatrix { // ... 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Structures & Algorithms","topic":"Graph Representation — Adjacency Matrix","title":"Graph Representation — Adjacency Matrix","description":"Master the adjacency matrix representation of graphs. Learn how to encode graph structure using 2D arrays, understand the O(V²) space complexity and O(1) edge lookup characteristics, and recognize when this representation is the optimal choice for your graph algorithms.","difficulty":"INTERMEDIATE","estimatedMinutes":60,"pages":[{"id":"seed_d8d840c3475a87ef5aa017567f60c225","title":"2D Array Representation","order":0,"content":[{"id":"opening-hook","title":"From Graph Abstraction to Concrete Data","content":[{"data":{"content":"In the previous modules, we established graphs as the most general structure for representing relationships between entities. We explored vertices, edges, directed and undirected connections, and weighted edges. But all of that was **abstract**—mathematical notation on paper.\n\nNow we face a critical question every engineer must answer: **How do we actually store a graph in computer memory?**\n\nThis question isn't merely academic. The choice of graph representation profoundly affects every algorithm you'll run on the graph. It determines memory consumption, the speed of common operations, and even which algorithms are practical to implement. Get this choice wrong, and you'll watch your graph algorithms crawl on datasets that should be handled easily.\n\nIn this module, we'll master the first and most elegant representation: **the adjacency matrix**—a simple yet powerful approach that encodes the entire graph structure in a two-dimensional array."},"type":"text"},{"data":{"icon":"Target","title":"What You Will Learn","content":"By the end of this page, you will deeply understand how to represent any graph as a 2D array, how the matrix structure maps to graph concepts, and how to construct adjacency matrices for directed, undirected, and weighted graphs. You'll be able to visualize the connection between the abstract graph and its matrix representation with complete clarity.","variant":"info"},"type":"callout"}]},{"id":"fundamental-insight","title":"The Fundamental Insight: Relationships as Grid Cells","content":[{"data":{"content":"The adjacency matrix representation is built on a beautifully simple insight: if we have **V vertices**, we can represent all possible edges between them using a **V × V grid**.\n\nThink about it this way. If you have 5 people at a party and want to track who has shaken hands with whom, you could create a 5×5 grid. Each row represents a person, each column represents a person, and the cell at row *i*, column *j* indicates whether person *i* has shaken hands with person *j*.\n\nThis is precisely what an adjacency matrix does for graphs. Every possible connection between any two vertices has a dedicated cell in the matrix. If the edge exists, we mark it (typically with 1 or the edge weight). If it doesn't exist, we use 0 or a special 'no edge' value."},"type":"text"},{"data":{"icon":"Info","title":"Why 'Adjacency' Matrix?","content":"The term 'adjacency' refers to the fact that two vertices are **adjacent** if there's an edge directly connecting them. The matrix answers the adjacency question: for any pair of vertices (i, j), are they adjacent? The answer is stored at position matrix[i][j].","variant":"note"},"type":"callout"},{"data":{"content":"**Formal Definition:**\n\nFor a graph **G = (V, E)** with vertices numbered 0 to V-1, the adjacency matrix **A** is a V × V matrix where:\n\n- For an **unweighted graph**: A[i][j] = 1 if there's an edge from vertex i to vertex j, and A[i][j] = 0 otherwise.\n\n- For a **weighted graph**: A[i][j] = w (the edge weight) if there's an edge from i to j with weight w, and A[i][j] = 0 (or ∞, or a sentinel value) if no edge exists.\n\nThis simple definition encapsulates the entire graph structure in a single data structure. The matrix IS the graph—every edge, every non-edge, completely encoded."},"type":"text"}],"titleType":"number","titleNumber":1},{"id":"undirected-matrix-construction","title":"Matrix Construction for Undirected Graphs","content":[{"data":{"content":"Let's build intuition by constructing an adjacency matrix step by step. Consider a simple undirected graph with 5 vertices (0, 1, 2, 3, 4) and the following edges:\n\n- 0 — 1\n- 0 — 2\n- 1 — 2\n- 1 — 3\n- 2 — 4\n- 3 — 4\n\n**Step 1: Create the empty V × V matrix**\n\nWe initialize a 5×5 matrix filled with zeros. Each row represents a 'from' vertex, each column represents a 'to' vertex."},"type":"text"},{"data":{"code":"Initial empty matrix (all zeros):\n\n 0 1 2 3 4 ← Column indices (destination vertices)\n ┌───┬───┬───┬───┬───┐\n 0 │ 0 │ 0 │ 0 │ 0 │ 0 │\n ├───┼───┼───┼───┼───┤\n 1 │ 0 │ 0 │ 0 │ 0 │ 0 │\n ├───┼───┼───┼───┼───┤\n 2 │ 0 │ 0 │ 0 │ 0 │ 0 │\n ├───┼───┼───┼───┼───┤\n 3 │ 0 │ 0 │ 0 │ 0 │ 0 │\n ├───┼───┼───┼───┼───┤\n 4 │ 0 │ 0 │ 0 │ 0 │ 0 │\n └───┴───┴───┴───┴───┘\n ↑\nRow indices (source vertices)","language":"text"},"type":"code"},{"data":{"content":"**Step 2: Add each edge by setting TWO cells**\n\nFor an undirected graph, each edge is bidirectional. The edge 0—1 means both 'vertex 0 connects to vertex 1' AND 'vertex 1 connects to vertex 0'. Therefore, we set BOTH matrix[0][1] = 1 AND matrix[1][0] = 1.\n\nThis produces a **symmetric matrix**—a critical property of adjacency matrices for undirected graphs."},"type":"text"},{"data":{"code":"After adding edge 0—1 (set [0][1] and [1][0]):\n\n 0 1 2 3 4\n ┌───┬───┬───┬───┬───┐\n 0 │ 0 │ 1 │ 0 │ 0 │ 0 │ ← Row 0: vertex 0 connects to vertex 1\n ├───┼───┼───┼───┼───┤\n 1 │ 1 │ 0 │ 0 │ 0 │ 0 │ ← Row 1: vertex 1 connects to vertex 0\n ├───┼───┼───┼───┼───┤\n 2 │ 0 │ 0 │ 0 │ 0 │ 0 │\n ├───┼───┼───┼───┼───┤\n 3 │ 0 │ 0 │ 0 │ 0 │ 0 │\n ├───┼───┼───┼───┼───┤\n 4 │ 0 │ 0 │ 0 │ 0 │ 0 │\n └───┴───┴───┴───┴───┘","language":"text"},"type":"code"},{"data":{"content":"**Step 3: Continue with remaining edges**\n\nFollowing the same process for all edges:"},"type":"text"},{"data":{"code":"Final adjacency matrix for the undirected graph:\n\n 0 1 2 3 4\n ┌───┬───┬───┬───┬───┐\n 0 │ 0 │ 1 │ 1 │ 0 │ 0 │ ← Vertex 0 connects to: 1, 2\n ├───┼───┼───┼───┼───┤\n 1 │ 1 │ 0 │ 1 │ 1 │ 0 │ ← Vertex 1 connects to: 0, 2, 3\n ├───┼───┼───┼───┼───┤\n 2 │ 1 │ 1 │ 0 │ 0 │ 1 │ ← Vertex 2 connects to: 0, 1, 4\n ├───┼───┼───┼───┼───┤\n 3 │ 0 │ 1 │ 0 │ 0 │ 1 │ ← Vertex 3 connects to: 1, 4\n ├───┼───┼───┼───┼───┤\n 4 │ 0 │ 0 │ 1 │ 1 │ 0 │ ← Vertex 4 connects to: 2, 3\n └───┴───┴───┴───┴───┘\n\nNotice: The matrix is symmetric along the main diagonal.\n A[i][j] = A[j][i] for all i, j — this is always true\n for undirected graphs.","language":"text"},"type":"code"},{"data":{"icon":"Lightbulb","title":"Visual Symmetry Check","content":"An easy way to verify correctness for undirected graphs: fold the matrix along the main diagonal (top-left to bottom-right). Both halves should match perfectly. If they don't, you've made an error or you're working with a directed graph.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":2},{"id":"directed-matrix-construction","title":"Matrix Construction for Directed Graphs","content":[{"data":{"content":"Directed graphs (digraphs) have edges with direction—an edge from vertex *i* to vertex *j* does NOT imply an edge from *j* to *i*. This changes how we construct the adjacency matrix.\n\nConsider a directed graph with 4 vertices (0, 1, 2, 3) and edges:\n\n- 0 → 1\n- 0 → 2\n- 1 → 2\n- 2 → 0\n- 2 → 3\n- 3 → 3 (a self-loop)\n\n**For directed graphs, we only set ONE cell per edge:** For an edge from *i* to *j*, we set A[i][j] = 1. We do NOT automatically set A[j][i]."},"type":"text"},{"data":{"code":"Directed graph adjacency matrix:\n\n 0 1 2 3\n ┌───┬───┬───┬───┐\n 0 │ 0 │ 1 │ 1 │ 0 │ ← From 0: edges go TO 1, TO 2\n ├───┼───┼───┼───┤\n 1 │ 0 │ 0 │ 1 │ 0 │ ← From 1: edge goes TO 2\n ├───┼───┼───┼───┤\n 2 │ 1 │ 0 │ 0 │ 1 │ ← From 2: edges go TO 0, TO 3\n ├───┼───┼───┼───┤\n 3 │ 0 │ 0 │ 0 │ 1 │ ← From 3: self-loop (goes TO itself)\n └───┴───┴───┴───┘\n\nNotice: The matrix is NOT symmetric.\n The '1' at [2][0] represents edge 2→0, but there's\n no '1' at [0][2] for edge 0→2 wait... actually there IS\n an edge 0→2, so [0][2]=1. Let me re-verify...\n\nCorrection: [0][2]=1 (edge 0→2 exists), [2][0]=1 (edge 2→0 exists)\nThese are two DIFFERENT edges, both present in this graph.","language":"text"},"type":"code"},{"data":{"content":"**Reading Convention (Critical!):**\n\nThe standard convention is:\n- **Row index = source vertex (FROM)**\n- **Column index = destination vertex (TO)**\n\nSo A[i][j] = 1 means there's an edge FROM i TO j.\n\nTo find all outgoing edges from vertex *i*: scan row *i* (all columns).\nTo find all incoming edges to vertex *j*: scan column *j* (all rows).\n\nThis convention is nearly universal, but always verify when reading graph code—some implementations flip the convention."},"type":"text"},{"data":{"icon":"AlertCircle","title":"Self-Loops Appear on the Diagonal","content":"A self-loop (an edge from a vertex to itself) is represented on the main diagonal. In our example, the self-loop 3→3 appears as A[3][3] = 1. For undirected graphs, self-loops contribute to the diagonal but are typically rare in most applications.","variant":"warning"},"type":"callout"}],"titleType":"number","titleNumber":3},{"id":"weighted-matrix-construction","title":"Weighted Graph Matrices","content":[{"data":{"content":"For weighted graphs, instead of storing 1 for 'edge exists', we store the **edge weight** in the corresponding cell. But this introduces a nuance: how do we distinguish between 'no edge' and 'edge with weight 0'?\n\n**Common Approaches:**\n\n1. **Use a sentinel value** — Store a special value like `∞` (infinity), `-1`, or `null` to indicate no edge. This is the most common approach.\n\n2. **Separate existence matrix** — Maintain two matrices: one for adjacency (0/1), one for weights. More memory but no ambiguity.\n\n3. **Assume non-negative weights** — If all weights are positive, use 0 or negative values for 'no edge'. Works, but limits the graphs you can represent."},"type":"text"},{"data":{"code":"Weighted directed graph example:\n\nEdges with weights:\n 0 → 1 (weight 5)\n 0 → 2 (weight 3)\n 1 → 2 (weight 2)\n 1 → 3 (weight 8)\n 2 → 3 (weight 1)\n\nAdjacency matrix (using ∞ for no edge):\n\n 0 1 2 3\n ┌─────┬─────┬─────┬─────┐\n 0 │ ∞ │ 5 │ 3 │ ∞ │\n ├─────┼─────┼─────┼─────┤\n 1 │ ∞ │ ∞ │ 2 │ 8 │\n ├─────┼─────┼─────┼─────┤\n 2 │ ∞ │ ∞ │ ∞ │ 1 │\n ├─────┼─────┼─────┼─────┤\n 3 │ ∞ │ ∞ │ ∞ │ ∞ │\n └─────┴─────┴─────┴─────┘\n\nThe shortest path from 0 to 3 is: 0 → 2 → 3 with total weight 4\n(We'll learn algorithms to compute this in later chapters!)","language":"text"},"type":"code"},{"data":{"icon":"Info","title":"Infinity in Practice","content":"In code, infinity is typically represented as MAX_INT, MAX_FLOAT, or a language-specific infinity constant. In Python: float('inf'). In JavaScript: Infinity. In Java: Integer.MAX_VALUE. Choose a value larger than any possible path weight to avoid algorithmic confusion.","variant":"note"},"type":"callout"},{"data":{"content":"**Weighted Undirected Graphs:**\n\nFor weighted undirected graphs, the matrix remains symmetric—both A[i][j] and A[j][i] store the same edge weight. An edge between vertices 0 and 1 with weight 5 means A[0][1] = A[1][0] = 5.\n\nThis symmetry property halves the information content (redundant storage), which we'll discuss in the space complexity section. For now, recognize that weighted undirected graphs follow the same symmetry rules as unweighted ones."},"type":"text"}],"titleType":"number","titleNumber":4},{"id":"code-implementation","title":"Implementation in Code","content":[{"data":{"content":"Let's translate these concepts into working code. We'll implement a complete adjacency matrix class that handles both weighted and unweighted graphs."},"type":"text"},{"data":{"code":"$72","title":"Adjacency Matrix Implementation","language":"typescript"},"type":"code"},{"data":{"content":"**Usage Examples:**"},"type":"text"},{"data":{"code":"// Create an undirected unweighted graph\nconst undirectedGraph = new AdjacencyMatrix(5, false);\nundirectedGraph.addEdge(0, 1); // Adds both 0→1 and 1→0\nundirectedGraph.addEdge(0, 2);\nundirectedGraph.addEdge(1, 3);\nundirectedGraph.addEdge(2, 4);\n\nconsole.log(undirectedGraph.hasEdge(0, 1)); // true\nconsole.log(undirectedGraph.hasEdge(1, 0)); // true (symmetric!)\nconsole.log(undirectedGraph.hasEdge(0, 4)); // false\n\n// Create a directed weighted graph\nconst directedGraph = new AdjacencyMatrix(4, true, Infinity);\ndirectedGraph.addEdge(0, 1, 5); // 0→1 with weight 5\ndirectedGraph.addEdge(0, 2, 3); // 0→2 with weight 3\ndirectedGraph.addEdge(1, 2, 2); // 1→2 with weight 2\n\nconsole.log(directedGraph.hasEdge(0, 1)); // true\nconsole.log(directedGraph.hasEdge(1, 0)); // false (directed!)\nconsole.log(directedGraph.getEdgeWeight(0, 1)); // 5\n\ndirectedGraph.print();\n// Output:\n// 0 1 2 3\n// 0: ∞ 5 3 ∞\n// 1: ∞ ∞ 2 ∞\n// 2: ∞ ∞ ∞ ∞\n// 3: ∞ ∞ ∞ ∞","title":"Using the Adjacency Matrix","language":"typescript"},"type":"code"},{"data":{"icon":"Lightbulb","title":"Initialization Matters","content":"Note how we initialize the matrix with all 'no edge' values in the constructor. This is O(V²) work, but it only happens once. The alternative—checking for undefined on every access—would slow down all operations and complicate the code.","variant":"tip"},"type":"callout"}],"titleType":"number","titleNumber":5},{"id":"main-diagonal","title":"The Main Diagonal: Self-Loops and Self-Connections","content":[{"data":{"content":"The main diagonal of an adjacency matrix—the cells where row index equals column index (A[0][0], A[1][1], A[2][2], etc.)—represents **self-loops**: edges from a vertex to itself.\n\nIn many applications, self-loops are either:\n\n1. **Impossible by definition** — A friendship network doesn't consider 'person is friends with themselves'\n2. **Implicitly true** — Every vertex is 'reachable from itself' in zero steps\n3. **Meaningful data** — A web page linking to itself, a state machine staying in the current state\n\n**Convention for the diagonal:**\n\n- For most graphs: A[i][i] = 0 (no self-loops)\n- For adjacency matrices used in matrix algorithms (like finding paths of length k): A[i][i] = 0 usually\n- For reflexive relations or graphs with self-loops: A[i][i] = 1 or the self-loop weight"},"type":"text"},{"data":{"code":"Adjacency matrix WITH self-loops:\n\n 0 1 2 3\n ┌─────┬─────┬─────┬─────┐\n 0 │ 1 │ 1 │ 0 │ 0 │ ← Self-loop at vertex 0\n ├─────┼─────┼─────┼─────┤\n 1 │ 1 │ 0 │ 1 │ 0 │ ← No self-loop at vertex 1\n ├─────┼─────┼─────┼─────┤\n 2 │ 0 │ 1 │ 1 │ 1 │ ← Self-loop at vertex 2\n ├─────┼─────┼─────┼─────┤\n 3 │ 0 │ 0 │ 1 │ 0 │ ← No self-loop at vertex 3\n └─────┴─────┴─────┴─────┘\n\nThe main diagonal (highlighted cells) shows self-loops.","language":"text"},"type":"code"},{"data":{"icon":"Info","title":"Diagonal and Undirected Graph Symmetry","content":"For undirected graphs, the diagonal doesn't affect symmetry. If A[i][i] = 1 (self-loop exists), it's trivially symmetric since A[i][i] = A[i][i]. The symmetry constraint A[i][j] = A[j][i] specifically matters for off-diagonal elements.","variant":"note"},"type":"callout"}],"titleType":"number","titleNumber":6},{"id":"reading-properties","title":"Reading Graph Properties from the Matrix","content":[{"data":{"content":"One powerful aspect of the adjacency matrix is how naturally it expresses graph properties. Let's explore what we can read directly from the matrix structure:"},"type":"text"},{"data":{"rows":[["Edge existence","Check if A[i][j] ≠ 0 (or ≠ ∞)","O(1)"],["Out-degree of vertex i","Count non-zero entries in row i","O(V)"],["In-degree of vertex i","Count non-zero entries in column i","O(V)"],["Total edges (directed)","Count all non-zero entries","O(V²)"],["Total edges (undirected)","(Count non-zero entries) / 2","O(V²)"],["Is graph undirected?","Check if A[i][j] = A[j][i] for all i,j","O(V²)"],["Has self-loops?","Check if any A[i][i] ≠ 0","O(V)"],["Isolated vertices","Rows (and columns) that are entirely zero","O(V²)"]],"caption":"Graph Properties from Adjacency Matrix","headers":["Property","How to Read from Matrix","Time Complexity"]},"type":"table"},{"data":{"content":"**Degree Sum Formula Verification:**\n\nRecall from graph theory: the sum of all vertex degrees equals twice the number of edges (for undirected graphs). With an adjacency matrix, this becomes: the sum of all entries in the matrix equals twice the edge count.\n\nThis provides a sanity check: if you add up every cell in an undirected graph's adjacency matrix and get an odd number, something is wrong—you've violated symmetry somewhere."},"type":"text"},{"data":{"code":"$73","title":"Extracting Graph Properties","language":"typescript"},"type":"code"}],"titleType":"number","titleNumber":7},{"id":"summary","title":"Summary: The 2D Array Representation","content":[{"data":{"content":"We've established a complete understanding of how graphs are represented using two-dimensional arrays. Let's consolidate the key concepts:"},"type":"text"},{"data":{"type":"ordered","items":["**An adjacency matrix is a V×V array** where A[i][j] indicates the edge from vertex i to vertex j.","**Unweighted graphs use binary values** — 1 for edge exists, 0 for no edge.","**Weighted graphs store edge weights** — with a sentinel value (∞, -1, null) for no edge.","**Undirected graphs produce symmetric matrices** — A[i][j] always equals A[j][i].","**Directed graphs may be asymmetric** — edge i→j doesn't imply edge j→i.","**Self-loops appear on the main diagonal** — A[i][i] ≠ 0 means vertex i has a self-loop.","**The matrix completely encodes the graph** — every possible edge has a dedicated cell."],"title":{"icon":"CheckCircle","text":"Key Takeaways","type":"icon","color":"primary","variant":"outline-circle"},"variant":"accent"},"type":"list"},{"data":{"content":"**Coming up next:**\n\nNow that we understand how the matrix is structured, we'll analyze its space consumption in detail. Why does it require O(V²) space? When is this acceptable, and when is it prohibitive? The next page dives deep into the space complexity analysis and its implications."},"type":"text"},{"data":{"icon":"CheckCircle","title":"Foundation Established","content":"You now understand how to represent any graph as a 2D array. You can construct adjacency matrices for directed, undirected, weighted, and unweighted graphs. You know the convention (row = from, column = to) and can read graph properties directly from the matrix structure. This foundation prepares you for complexity analysis and algorithm implementation.","variant":"success"},"type":"callout"}],"titleType":"number","titleNumber":8}],"isLocked":false},{"id":"seed_f52cc8ee4c6c351cc8090f5f3981d364","title":"Space Complexity — O(V²)","order":1,"content":null,"isLocked":true},{"id":"seed_8f1928972542e3eaa876f0fcf42e30fd","title":"Edge Lookup — O(1)","order":2,"content":null,"isLocked":true},{"id":"seed_f3376e5ee9aca2eb0ed5afe059cbaadb","title":"When Matrices Are Appropriate","order":3,"content":null,"isLocked":true}]}},"dataUpdateCount":1,"dataUpdatedAt":1792313192528,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getModule"],{"input":{"slug":"graph-representation-adjacency-matrix"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getModule\"],{\"input\":{\"slug\":\"graph-representation-adjacency-matrix\"},\"type\":\"query\"}]"},{"dehydratedAt":1792313192577,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792313192528,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["learningContent","getProgress"],{"input":{"moduleId":"seed_0ba7d54558b51541440abdb96c9f86f1"},"type":"query"}],"queryHash":"[[\"learningContent\",\"getProgress\"],{\"input\":{\"moduleId\":\"seed_0ba7d54558b51541440abdb96c9f86f1\"},\"type\":\"query\"}]"},{"dehydratedAt":1792313192577,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792313192528,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["feedback","get"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_f52cc8ee4c6c351cc8090f5f3981d364"},"type":"query"}],"queryHash":"[[\"feedback\",\"get\"],{\"input\":{\"contentId\":\"seed_f52cc8ee4c6c351cc8090f5f3981d364\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792313192577,"state":{"data":{"json":null},"dataUpdateCount":1,"dataUpdatedAt":1792313192528,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["feedback","getUserLike"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_f52cc8ee4c6c351cc8090f5f3981d364"},"type":"query"}],"queryHash":"[[\"feedback\",\"getUserLike\"],{\"input\":{\"contentId\":\"seed_f52cc8ee4c6c351cc8090f5f3981d364\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792313192577,"state":{"data":{"json":[]},"dataUpdateCount":1,"dataUpdatedAt":1792313192528,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"success","fetchStatus":"idle"},"queryKey":[["highlights","getHighlights"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_f52cc8ee4c6c351cc8090f5f3981d364"},"type":"query"}],"queryHash":"[[\"highlights\",\"getHighlights\"],{\"input\":{\"contentId\":\"seed_f52cc8ee4c6c351cc8090f5f3981d364\",\"contentType\":\"LEARNING_PAGE\"},\"type\":\"query\"}]"},{"dehydratedAt":1792313192577,"state":{"data":"$undefined","dataUpdateCount":0,"dataUpdatedAt":0,"error":null,"errorUpdateCount":0,"errorUpdatedAt":0,"fetchFailureCount":0,"fetchFailureReason":null,"fetchMeta":null,"isInvalidated":false,"status":"pending","fetchStatus":"fetching"},"queryKey":[["highlights","getPopularHighlights"],{"input":{"contentType":"LEARNING_PAGE","contentId":"seed_f52cc8ee4c6c351cc8090f5f3981d364","minCount":2},"type":"query"}],"queryHash":"[[\"highlights\",\"getPopularHighlights\"],{\"input\":{\"contentId\":\"seed_f52cc8ee4c6c351cc8090f5f3981d364\",\"contentType\":\"LEARNING_PAGE\",\"minCount\":2},\"type\":\"query\"}]","promise":"$@74"}]},"children":"$L75"}]