Graph theory is a branch of mathematics that studies the relationships between objects in a given set. This is done using structures called graphs, G(V,A), where V is a non- empty of objects called vertices and A is a set of unordered pairs of V, called edges.

Depending on the application, edges may or may not have direction, edges may or may not be allowed to connect a vertex to itself, and vertices and/or edges may have an associated (numerical) weight.

Graph theory is a mathematical tool for characterizing a network ; in this way, it is possible to study the properties and the temporal and spatial development of a set of related elements.

Graph theory is a fundamental tool for resource management, transportation planning, and optimization , being applied to various problems, such as location and route planning problems for different types of services, the study of DNA structure, and code design, electrical interconnection, and molecular engineering (BOAVENTURA and JURKIEWICZ, 2009).

Among the graph substructures that offer solutions to applied problems, paths stand out especially for their potential associated with traffic, transportation, and location problems in discrete systems (BOAVENTURA NETTO, 2006).11

Search and Graph Theory

Graph search is one of the most widely used techniques for designing graph algorithms. In such searches, the order in which the vertices of a graph are visited defines an enumeration of the graph's vertices and a characterization of these enumerations which, according to the search strategy used , has proven important in graph algorithm applications. In this work, we generalize the concept of search and the characterizations, well known in the case of graphs, to the case of hypergraphs.²

Introduction to Graph Theory

We introduced the concept of a graph, a representation of elements and the relationships between them through vertices and links (or edges). We presented two seemingly unrelated problems that can be visualized using graphs. The first is the famous Königsberg Bridges problem, and the second asks to show that in any group there are two people who have the same number of friendships within the group.

Graph Theory and SEO

Semantic SEO is highly related to strategies that connect information through semantically qualified links. Whether creating internal links between entities content page reputation and the relevance of the content to be indexed.

With this in mind, we can use graphs as a basis for creating an internal linking strategy that will help search engines navigate your site , understanding its content and crawling all pages correctly.

We execute internal linking projects to strategically and controllably link all pages on a single website. It's extremely important to avoid two things in a website's structure: orphan pages (pages not connected to any other pages) or deep pages (pages that are many clicks away from the homepage).

Therefore, simplifying the connection between pages, via links, makes it easier for your visitors to navigate your website and helps search engine bots understand your content based on how those pages are linked.

How do I execute the project?

Using a Hub

The most important feature of a Hub is its role as the official focal point for connecting to semantically related content. This strategy is crucial because it defines topics and groups content around them, helping search engines understand each Hub.

Links with a purpose

Search engine algorithms don't need direct links between all pages to understand the relationship between the topics of two pieces of content (whether websites or pages). Creating a taxonomy for your link building project is an important step in strategically structuring the project, avoiding creating connections between semantically separate content. But you need to avoid creating links artificially; instead of helping, these will harm your SEO.

¹ PROPOSAL FOR A COLLECTION MODEL FOR THE REVERSE CHANNEL OF POST-CONSUMER PAPER ON A UNIVERSITY CAMPUS BASED ON GRAPH THEORY - Revista Produção Online, Florianópolis, SC, v.13, n. 4, p. 1543-1568, Oct./Dec. 2013. Accessed June 22, 2021 at
 https://producaoonline.org.br/rpo/article/view/1526/1094 ² - Bragatto; Donadelli and Guedes in Extensions and characterizations of searches for hypergraphs with multiple edges - Vol. 8, no. 2; pp. 16 – 27 - https://doaj.org/article/0cd76c68babc417183f576b0b08f28c7 . Accessed on June 22, 2021

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