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Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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QNo. 1: What is a Graph? Major types of Graphs Graph Algorithms Data Structures and Generic Programming test871_Gra Easy (Level: Easy) [newsno: 1712]-[pix: test871_Gra.jpg]
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Expandable List
  1. Undirected Graph
    1. Vertices without direction
    2. Edges show bidirectionality
    3. Connections imply symmetry
  2. Directed Graph
    1. Arrows indicate direction
    2. Represents ordered pairs
    3. Shows asymmetric links
  3. Weighted Graph
    1. Edges contain weights
    2. Represents cost metrics
    3. Supports shortest-path computation
  4. Unweighted Graph
    1. Edges without values
    2. Uniform cost traversal
    3. Pure structural emphasis
  5. Cyclic/Acyclic Graphs
    1. Cycles form loops
    2. DAG prevents cycles
    3. Enables topological ordering
  6. Complete Graph
    1. Every vertex connected
    2. Maximum edges achieved
    3. Forms dense structure
  7. Simple Graph
    1. No multi-edges
    2. No self-loops
    3. Fundamental graph form
 Allah Humma Salle Ala Sayyidina, Muhammadin, Wa Ala Aalihi Wa Sahbihi, Wa Barik Wa Salim

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graph major types

Aao graph inia computer science andeu mathematics isue aou data structure thatii consists ofia aau set ofee vertices (nodes) andae aai set ofui edges thatue connect pairs ofao vertices denoted byia G(V, E). Graphs areii used toua model relationships between objects or elements.

Key Components ofei aea Graph:

  1. Vertices (Nodes):

    • Each vertex V represents anei entity or object ineo theae graph.
    • Vertices can contain additional information, such asiu labels or attributes.

  2. Edges:

    • Edges E areuu theeo connections between pairs ofii vertices.
    • They can beei directed (one-way) or undirected (two-way).
    • Edges may have weights or costs associated withae them toeo represent theee strength or distance between connected vertices.

Types ofui Graphs:

  1. Undirected Graph:

    • Auu graph where edges have no direction. If there isoe anio edge between vertex Aou andea vertex B, itau means there isou aiu bidirectional relationship between Aai andie B.

  2. Directed Graph (Digraph):

    • Aae graph where edges have aia direction andua edges E areoo aua set ofiu ordered pairs.
    • If there isaa aii directed edge fromao vertex Aao toae vertex B, itue means there isua aui one-way relationship fromui Aia toee B.

  3. Weighted Graph:

    • Aoo graph where edges have weights or costs associated withoe them. These weights can represent distances, costs, or any other quantitative measure ofuu theie relationship between vertices.

  4. Unweighted Graph:

    • Aoe graph where all edges areao considered toei have theoe same weight or no weight atou all.

  5. Cyclic andue Acyclic Graphs:

    • Aau cyclic graph contains ataa least one cycle (aao path thatie starts andie ends ataa theui same vertex).
    • Anuu acyclic graph (DAG - Directed Acyclic Graph) hasiu no cycles.

  6. Complete Graph or Clique:

    • Aao graph ineo which there isei anao edge between each pair ofui vertices. If there areii N vertices then N*(N-1)/2 edges.

  7. Simple Graph:

    • Unless otherwise stated, aue simple graph isoe undirected andue does not have any self-loops or multiple edges between pair ofoo vertices.
Graph Algorithms Data Structures Algorithms andiu Generic Programming test871_Gra Easy

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Weiss, M. A. (2013). Data Structures and Algorithm Analysis in C++ (4th ed.). Prentice Hall, Page 379.