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Knowledge
Graphs are crucial mathematical structures for modeling problems, requiring efficient representation for algorithmic solutions. Various methods exist for representing graphs, including adjacency matrices and adjacency lists, each with distinct advantages and disadvantages regarding space and operational efficiency. Understanding these graph representations and their applications forms the foundation for algorithmic problem-solving in computer science.
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Sections
References
ch19.pdfClass Notes
Memorization
What we have learnt
- Graphs consist of vertices ...
- Adjacency matrices offer a ...
- Adjacency lists provide a m...
Final Test
Revision Tests
What we have learnt
- Graphs consist of vertices connected by edges, which can be directed or undirected.
- Adjacency matrices offer a straightforward representation but can be space-inefficient in sparse graphs.
- Adjacency lists provide a more compact representation but may require scanning through neighbors to determine connectivity.
Key Concepts
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Term: Graph
Definition: A collection of vertices connected by edges.
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Term: Directed Graph
Definition: A graph where edges have a direction, represented as ordered pairs.
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Term: Undirected Graph
Definition: A graph where edges do not have direction, represented as unordered pairs.
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Term: Adjacency Matrix
Definition: A square matrix used to represent a graph, where the entry at row i and column j indicates the presence of an edge between vertices i and j.
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Term: Adjacency List
Definition: A representation of a graph where each vertex has a list of its neighbors.
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Term: BreadthFirst Search (BFS)
Definition: An algorithm for traversing graphs where all neighbors at the current depth are explored before moving on to nodes at the next depth level.