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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<meta name="description" content="">
<meta name="author" content="">
<title>Components</title>
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<div class="container">
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<img src="images\logo.png" alt="" height="100px" width="100px">
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<a class="nav-link click-scroll" href="index.html#section_1">Home</a>
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<a class="nav-link click-scroll" href="index.html#section_2">Browse Topics</a>
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<a class="nav-link click-scroll" href="index.html#section_3">How it works</a>
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<li class="breadcrumb-item active" aria-current="page">COMPONENTS/USES </li>
</ol>
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<h2 class="text-white">Components and Uses of Graphs </h2>
<div class="d-flex align-items-center mt-5">
<a href="#topics-detail" class="btn custom-btn custom-border-btn smoothscroll me-4">Read
More</a>
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<h3 class="mb-4">Components:</h3>
<p><strong>1. Vertices (Nodes):</strong>
<ul>
<li>
Definition: Fundamental units of a graph, representing entities.
</li>
<li>Representation: Usually denoted as V. Each vertex can have a label (in labeled graphs)
or be anonymous (in unlabeled graphs).</li>
</ul>
</p>
<p><strong>2.Edges (Links/Arcs):</strong>
<ul>
<li>
Definition: Connections between pairs of vertices
</li>
<li>Representation: Usually denoted as E. Each edge can be directed or undirected, and may
carry a weight in weighted graphs.</li>
</ul>
</p>
<p><strong>3.Adjacency:</strong>
<ul>
<li>
Definition: Relationship between vertices connected by an edge.
</li>
<li>Representation: Can be depicted using adjacency lists, adjacency matrices, or incidence
matrices.</li>
</ul>
</p>
<p><strong>4.Degree:</strong>
<ul>
<li>
The number of edges connected to a vertex.
</li>
</ul>
</p>
<p><strong>5. Paths:</strong>
<ul>
<li>
A sequence of vertices connected by edges.
</li>
</ul>
</p>
<p><strong>6. Connected Components:</strong>
<ul>
<li>
Subsets of vertices such that there is a path between any two vertices in the subset.
</li>
<li>Types:
<ul type="solid">
<li>Strongly Connected Component (in Directed Graphs): Every vertex is reachable
from every other vertex.</li>
<li>Weakly Connected Component: Ignoring edge directions, every vertex is reachable
from every other vertex.</li>
</ul>
</li>
</ul>
</p>
<p><strong>7.Subgraphs:</strong>
<ul>
<li>
A subset of a graph’s vertices and edges that forms a graph.
</li>
</ul>
</p>
<br>
<h3 class="mb-4">Uses of Graphs:</h3>
<p><strong>1.Computer Science:</strong>
<ul>
<li>
Network Design: Routing, network topology, internet structure.
</li>
<li>Data Organization: Representing file systems, databases (ER diagrams).</li>
</ul>
</p>
<p><strong>2.Social Networks:</strong>
<ul>
<li>
Modeling Relationships: Friendships, followers, connections.
</li>
<li>Community Detection: Identifying groups of closely connected users.</li>
</ul>
</p>
<p><strong>3.Transportation and Logistics:</strong>
<ul>
<li>
Route Planning: Finding shortest paths, optimal routes.
</li>
<li>Traffic Flow: Modeling and optimizing traffic systems.</li>
</ul>
</p>
<p><strong>4.Biology and Chemistry:</strong>
<ul>
<li>
Gene Regulation Networks: Understanding gene interactions.
</li>
<li>Protein-Protein Interaction Networks: Studying interactions between proteins.</li>
</ul>
</p>
<p><strong>5.Engineering:</strong>
<ul>
<li>
Circuit Design: Representing electrical circuits.
</li>
<li>Structural Analysis: Analyzing forces and stresses in structures.</li>
</ul>
</p>
</div>
</div>
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</section>
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