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Nov 9, 2024 · Graph algorithms are methods used to manipulate and analyze graphs, solving various range of problems like finding the shortest path, cycles detection. If you are looking for difficulty-wise list of problems, please refer to Graph Data Structure. Basics of Graph: Introduction to Graphs; Graph and its representations; Transpose graph; BFS and ...
- Set 1
A register array is a collection of contiguous registers in...
- Vertex Cover Problem
Consider all the subset of vertices one by one and find out...
- Shortest Path in an Unweighted Graph
Approach: The idea is to use a modified version of...
- Introduction to Graphs
Graph Data Structure is a non-linear data structure...
- K Centers Problem
A vertex cover of an undirected graph is a subset of its...
- Rat in a Maze
We have discussed Backtracking and Knight’s tour problem in...
- A Peterson Graph Problem
The following graph G is called a Petersen graph and its...
- Cycles of Length N in an Undirected and Connected Graph
Wheel Graph: A Wheel graph is a graph formed by connecting a...
- Set 1
In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph theory within mathematics. A graph data structure consists of a finite (and possibly mutable) set of vertices (also called nodes or points), together with a set of unordered pairs of these ...
- Overview
- The Basics of Graph Theory
- Types of Graphs
- Conclusions
In this tutorial, we’ll discuss some of the most important data structures in computer science – graphs. We’ll first study the basics of graph theory, in order to familiarize ourselves with its conceptual foundation. We’ll then study the types of graphs that we can find in our machine learning applications. At the end of this tutorial, we’ll know w...
2.1. The Definition of a Graph
A graph is a structurethat comprises a set of vertices and a set of edges. So in order to have a graph we need to define the elements of two sets: vertices and edges. The vertices are the elementary units that a graph must have, in order for it to exist. It’s customary to impose on graphs the condition that they must have at least one vertex, but there’s no real theoretical reason why this is the case. Vertices are mathematical abstractions corresponding to objects associated with one another...
2.2. General Properties of Vertices
We’re now going to focus in more detail about what characteristics vertices and edges possess. Let’s start with the vertices first. As stated before, graphs need vertices but don’t necessarily require edges. In fact, it’s perfectly possible to have graphs composed entirely by vertices. Vertices that aren’t connected to any others, such as those of the empty graphs, are called isolated: We also say that isolated vertices have a degree equal to zero. Degree, in this context, indicates the numbe...
2.3. Labels of Vertices
Vertices can also have values associated with them. These values can take any format and there are no specific restrictions for them. A vertex with an associated value is called a labeled vertex, while a vertex with no associated value is called unlabeled: In general, we can distinguish any two unlabeled vertices exclusively on the basis of their paired vertices. The comparison between labeled vertices requires us instead to study both the pairs of vertices and the values assigned to them: On...
3.1. The Empty Graph
We mentioned before that graphs exist only if their set of vertices is not null. Their set of edges, however, may as well be empty. If this is the case, we say that the graph is empty: An empty graph has always size .
3.2. The Directed Graph
As anticipated above, a directed graph is a graph that possesses at least one edge between two vertices and which doesn’t have a corresponding edge connecting the same vertices in the opposite direction. Directed graphs have the characteristic that they model real-world relationships well for which we can’t freely interchange the subject and the object. As a general rule, if we aren’t sure whether a graph should be directed or undirected, then the graph is directed: We can only traverse direc...
3.3. The Undirected Graph
Undirected graphs are graphs for which the existence of any edge between the vertices implies the presence of a corresponding edge : Undirected graphs allow their traversal between any two vertices connected by an edge. The same isn’t necessarily true for directed graphs.
In this tutorial, we studied the conceptual bases of graph theory. We also familiarized ourselves with the definitions of graphs, vertices, edges, and paths. We’ve also studied the types of graphs that we can encounter and what are their predictable characteristics in terms of vertices, edges, and paths.
- Gabriele De Luca
Aug 5, 2024 · Applications of Graph Theory: In mathematics and computer science, a graph is a mathematical structure that consists of two main components: vertices (or nodes) and edges. The study of these graphs in various contexts is called graph theory. There are various applications of graph theory in real life such as in computer graphics and networks, biolo
- Finite Graphs. A graph is said to be finite if it has a finite number of vertices and a finite number of edges. A finite graph is a graph with a finite number of vertices and edges.
- Infinite Graph: A graph is said to be infinite if it has an infinite number of vertices as well as an infinite number of edges.
- Trivial Graph: A graph is said to be trivial if a finite graph contains only one vertex and no edge. A trivial graph is a graph with only one vertex and no edges.
- Simple Graph: A simple graph is a graph that does not contain more than one edge between the pair of vertices. A simple railway track connecting different cities is an example of a simple graph.
May 26, 2023 · In computer science, a graph is an abstract representation of a set of objects, known as vertices or nodes, connected by a set of edges. Graphs offer a flexible way to depict relationships and ...
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In mathematics and computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines).
