Graph Representations

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The three main ways to represent a graph in memory, each with different space and time tradeoffs for common operations.

Key Properties

• Adjacency List
• Adjacency Matrix
• Edge List

Tradeoffs

• Adjacency list — O(V+E) space, efficient for sparse graphs.
• Adjacency matrix — O(V²) space, O(1) edge lookup, better for dense graphs.
• Edge list — simplest, O(E) space, slow lookups.

Related

• Directed vs Undirected Graphs
• Special Graphs
• Algorithms (graph algorithms operate on these)

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data-structures graphs representations