Graphs vs Trees Quiz
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Questions and Answers

What is a graph in the context of data structures?

  • A hierarchical data structure with a single root node
  • A data structure with a fixed number of edges
  • A type of tree with only two nodes
  • A finite set of nodes with edges between nodes (correct)

    • What is the primary difference between a tree and a graph?

  • Graphs have a single root node, while trees do not
  • Trees are a special case of graphs with no loops (correct)
  • Graphs are always connected, while trees are not
  • Trees are used in social networks, while graphs are used in maps

    • What is a key characteristic of the edges in a tree?

  • Each node can have any number of edges
  • There are always n-1 edges in a tree with n nodes (correct)
  • There is always a single edge between each node
  • Edges are always directed in a tree

    • What type of relationship exists between nodes in a tree?

    <p>Parent-child relationships with each node having one parent</p> Signup and view all the answers

    What is a common application of graphs?

    <p>Social networks and maps</p> Signup and view all the answers

    What is a key feature of a graph that distinguishes it from a tree?

    <p>Graphs can have cycles and disconnected components</p> Signup and view all the answers

    What does each relationship in a graph represent?

    <p>Edges between entities x and y</p> Signup and view all the answers

    What is an individual data element of a graph called?

    <p>Vertex</p> Signup and view all the answers

    What is a weighted edge?

    <p>An edge with a cost on it</p> Signup and view all the answers

    What is a self-loop?

    <p>An edge that connects a vertex to itself</p> Signup and view all the answers

    What is a connected graph?

    <p>A graph with a path between every pair of nodes</p> Signup and view all the answers

    What is the indegree of a node?

    <p>The number of edges connecting to the node</p> Signup and view all the answers

    Study Notes

    Definition and Basics of Graphs

    • A graph is a non-linear data structure consisting of a finite set of nodes with edges between them.
    • A graph G can be formally represented as (V, E), where V is a finite set of nodes, and E is a set of pairs of nodes.

    Graph vs. Tree

    • A tree is a connected graph with no loops or cycles.
    • Graphs can have cycles and disconnected components, while trees are connected with no cycles.
    • In a tree, each node (except the root) has exactly one parent, whereas in a graph, nodes can have multiple parents or no parents.

    Node and Edge Relationships

    • Nodes (or vertices) represent entities such as people, cities, computers, words, etc.
    • Edges (x, y) represent relationships between entities x and y, such as distance, friendship, child-parent relationships, etc.

    Graph Terminology

    • A vertex (or node) is an individual data element of a graph.
    • An edge is a connecting link between two vertices and can be undirected, directed, or weighted.
    • Undirected edges are bidirectional, while directed edges are unidirectional.
    • Weighted edges have a cost or value associated with them.

    Edge Types and Graph Properties

    • Parallel edges or multiple edges have the same endpoints.
    • A self-loop is an edge that connects a node to itself.
    • A simple graph has no parallel or self-loop edges.
    • Adjacent nodes are connected by an edge.
    • A path is a sequence of vertices that connect two nodes in a graph.

    Graph Connectivity

    • An undirected graph is connected if there is a path between every pair of nodes.
    • A disconnected graph is one where there is no path between some pair of nodes.

    Indegree and Graph Types

    • The indegree of a node is the number of edges incident to it.
    • Types of graphs include undirected, directed, complete, and weighted graphs.

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    Description

    Test your understanding of graphs and trees with this quiz. Learn about the differences between graphs and trees, including their structures and characteristics.

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