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We start with the classical model proposed by Barab\u00e1si and Albert: nodes are added to the network connecting preferably to nodes that are more connected. We also present models that consider more representative elements from social perspectives, such as the homophily between the nodes and the fitness that each node has, to build connections. Furthermore, we show a version of these models that includes Euclidean distance between the nodes as a preferential attachment component. Our objective is to study the fundamental properties of these networks, as distribution of connectivity, degree correlation, shortest path, cluster coefficient and how these characteristics are affected by the preferential attachment rules. In addition to the review, we also provided an application of these models using real-world networks.<\/jats:p>","DOI":"10.1093\/comnet\/cnab008","type":"journal-article","created":{"date-parts":[[2021,3,3]],"date-time":"2021-03-03T20:23:24Z","timestamp":1614803004000},"source":"Crossref","is-referenced-by-count":24,"title":["Networks with growth and preferential attachment: modelling and applications"],"prefix":"10.1093","volume":"9","author":[{"given":"Gabriel G","family":"Piva","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Federal de Lavras, 37200-900 Lavras, MG, Brazil and Departamento de Fisica, Pontif\u00edcia Universidade Cat\u00f3lica do Rio de Janeiro, 22451-900 Rio de Janeiro, RJ, Brazil"}]},{"given":"Fabiano L","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Federal de Lavras, 37200-900 Lavras, MG, Brazil"}]},{"given":"Ang\u00e9lica S","family":"Mata","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade Federal de Lavras, 37200-900 Lavras, MG, Brazil"}]}],"member":"286","published-online":{"date-parts":[[2021,4,12]]},"reference":[{"key":"2021070819455179800_B1","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1126\/science.286.5439.509","article-title":"Emergence of scaling in random networks","volume":"286","author":"Barab\u00e1si,","year":"1999","journal-title":"Science"},{"key":"2021070819455179800_B2","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1080\/00107510500052444","article-title":"Power laws, Pareto distributions and Zipf\u2019s law","volume":"46","author":"Newman,","year":"2005","journal-title":"Contemp. 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