Struktura podataka grafikona i Algorithms (Primjer)

Što je graf u strukturi podataka?

A graph is a non-linear data structure that consists of vertices and edges, where vertices contain the information or data, and the edges work as a link between a pair of vertices.

It is used to solve real-world problems like finding the best route to the destination location and the route for telecommunications and social networks. Users are considered a node in the Graph, and the wires are the edges connecting the users.

Ako su bridovi predstavljeni kao E, a vrhovi kao V, tada se graf G može napisati kao skup vrhova i bridova, kao što je G (V, E).

Primjer grafikona u strukturi podataka

Here is a simple example of a graph data structure:

It is a simple undirected graph (one kind of Graph). Here the set of vertices is: {A, B, C, D, E, F}. Two vertices create an edge. For example, A and B are linked with an edge. However, A and F are not linked with any edges.

Terminologije grafova u strukturi podataka

The following are some important terms used in the graph data structure:

Termin	Description
Tjeme	Each data element is called a vertex or a node. In the above image, A, B, C, D & E are the vertices.
Rub (luk)	Connecting links between two nodes or vertices are called an edge (Arc). It has two ends and is represented as (startingVertex, endingVertex).
Neusmjereni rub	To je dvosmjerni rub.
Usmjerena oštrica	To je jednosmjerni rub.
Ponderirani rub	An edge with a value on it.
Stepen	In a Graph, the number of edges connected to a vertex is called a degree.
Indegree	Ukupan broj dolaznih bridova povezanih s vrhom.
Outdegree	Ukupan broj izlaznih bridova povezanih s vrhom.
Samopetlja	Brid se naziva samopetlja ako se njegove dvije krajnje točke podudaraju.
Susjedstvo	Vertices are said to be adjacent if an edge is connected between them.

Vrste grafova u strukturi podataka

Ovdje je popis najčešćih vrste grafova u strukturi podataka:

• Usmjereni graf
• Neusmjereni graf
• Ponderirani grafikon
• Dvosmjerni graf
• Beskonačni graf
• Null Graph
• Trivijalni graf
• Višestruki grafikon
• Kompletan grafikon
• Povezani graf
• Ciklički graf
• Usmjereni aciklički graf (DAG)
• Grafikon ciklusa
• Bipartitni graf
• Eulerov graf
• Hamiltonov graf

How to Represent a Graph in Data Structure?

A graph is commonly stored in memory using one of two representations. The choice affects how much memory the graph uses and how fast common operations run.

• Matrica susjednosti: A two-dimensional V × V array where cell [i][j] is 1 (or the edge weight) if an edge exists between vertex i and vertex j, and 0 otherwise. It allows O(1) edge lookup but uses O(V²) space, making it best for dense graphs.
• Popis susjedstva: An array of lists where each vertex stores a list of its neighbouring vertices. It uses O(V + E) space and is efficient for sparse graphs, which is why most real-world graphs use it.

You can read more about these in the adjacency list and matrix representation of a graph udžbenik.

Primjene strukture podataka grafikona

A graph has many use cases. There are a lot of algorithms that use Graphs. Here are some of the applications of the Graph:

• Google Maps uses graphs to find the intersection of two roads and calculate the distance between two locations. For example, Dijkstra, for finding the shortest distance between the source and destination location.
• Facebook uses Graphs to find the mutual friends of the users. Its algorithm considers each user as a node of a graph.
• For resource allocation, a DAG (Directed Acyclic Graph) is used. It checks the dependency of the resources.
• The Google Tražilice koriste grafove za izradu rangiranja web stranica.
• Kartaping Uređaj koristi strukturu podataka grafa.
• A usmjerivač and its protocol use the Graph to learn the path to the destination.

Pitanja i odgovori