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Questions and Answers
Explain the components of a graph and their alternative names.
Explain the components of a graph and their alternative names.
The components of a graph are vertices (also known as nodes) and edges (also known as lines or arcs).
What are the two most common ways to represent a graph?
What are the two most common ways to represent a graph?
The two most common ways to represent a graph are Adjacency Matrix and Adjacency List.
How is an adjacency matrix used to represent a graph?
How is an adjacency matrix used to represent a graph?
An adjacency matrix is a matrix of boolean values (0s and 1s) where if there is an edge from vertex i to j, adjMat[i][j] is marked as 1, and if there is no edge, it is marked as 0.
What is the purpose of an adjacency list in graph representation?
What is the purpose of an adjacency list in graph representation?
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Define a directed graph and explain how edges are represented in a directed graph.
Define a directed graph and explain how edges are represented in a directed graph.
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Study Notes
Components of a Graph
- Vertices (or Nodes): Fundamental units in a graph that represent entities such as locations or objects.
- Edges (or Links): Connections between vertices that illustrate relationships, showing how two nodes are associated.
- Weighted Edges: Edges that have associated values or weights, indicating the cost or distance between connected vertices.
- Directed Edges: Edges that have a direction, showing a one-way relationship from one vertex to another.
Common Representations of a Graph
- Adjacency Matrix: A square matrix used to represent a graph, where the rows and columns represent vertices. An entry of '1' indicates an edge between vertices, while '0' indicates no connection.
- Adjacency List: A collection of lists or arrays where each vertex has a list of adjacent vertices, effectively showing which vertices are directly connected.
Adjacency Matrix Usage
- Represents the presence or absence of edges between all pairs of vertices in a graph efficiently.
- Enables quick checks for the existence of an edge but can use significant space for sparse graphs.
Purpose of an Adjacency List
- Provides a space-efficient way to represent sparse graphs, where many vertex pairs do not have edges.
- Facilitates easy traversals and operations like adding or removing edges due to its dynamic nature.
Directed Graph Definition
- A directed graph has edges with an orientation, meaning relationships flow in a specific direction from one vertex (the source) to another (the target).
- Each directed edge is often represented as an ordered pair of vertices, indicating the direction of the connection.
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Description
Learn about the non-linear data structure called a graph, which consists of vertices and edges. Explore the components of a graph including vertices and edges, and how they are denoted in formal notation. Gain insights into the fundamental units of graphs and their labels.
