ANALYSIS OF THE BRAZILIAN STOCK MARKET THROUGH GRAPH CENTRALITY MEASURES

Finkel, Mariana Duque; Del-Vecchio, Renata R.

doi:10.1590/0101-7438.2021.041.00248549

Mariana Duque Finkel ^**Corresponding author

Universidade Federal Fluminense - UFF, RJ, Brazil - E-mail: mariana duque@id.uff.br

http://orcid.org/0000-0001-5220-0715

Renata R. Del-Vecchio

Universidade Federal Fluminense - UFF, RJ, Brazil - E-mail: rrdelvecchio@id.uff.br

http://orcid.org/0000-0003-1400-2309

*Corresponding author

Thumbnail

Figure 1
Example of balanced and unbalanced signed graph.

Thumbnail

Figure 2
Example of graph with degree distribution that follows a Power Law as described by ^{Boginsky et al. (2005}6. BOGINSKY V, BUTENKO S & PARDALOS P. 2005. Statistical Analysis of Financial Networks. Computational Statistics and Data Analysis, 48: 431-443.).

Thumbnail

Figure 3
Distribution of degree of shares for the years 2018, 2019 and 2020.

Thumbnail

Figure 4
Distribution of the degree of shares for different values of θ for the year 2018.

Thumbnail

Figure 5
Distribution of the degree of shares for different values of θ for the year 2019.

Thumbnail

Figure 6
Distribution of the degree of shares for different values of θ for the year 2020.

Thumbnail

Table 1
Relevance Factors in 2018.

Thumbnail

Table 2
Relevance Factors in 2019.

Thumbnail

Table 3
Relevance Factors in 2020.

Thumbnail

Table 4
Position and values of the first and last positions of the centralities.

Thumbnail

Table 5
Position and Centrality of the most central shares in 2018.

Thumbnail

Table 6
Position and Centrality of the most central shares in 2019.

Thumbnail

Table 7
Position and Centrality of the most central shares in 2020.

Thumbnail

SHARE COMPANY NAME ECONOMIC ACTIVITY ABEV3 Ambev SA Non-Cyclical Consumption / Beverages / Beers and Soft Drinks ALPA4 Alpargatas SA Cyclic Consumption / Fabrics, Apparel and Footwear / Apparel ALSO3 Aliansce Sonae Shopping Centers SA Finance / Property Exploration / Property Exploration AMAR3 Marisa Lojas SA (LOJAS MARISA) Cyclic Consumption / Trade / Fabrics, Apparel and Footwear AZUL4 Azul SA Industrial Goods / Transport / Air Transport B3SA3 B3 SA Brasil Bolsa Balcão Financial / Miscellaneous Financial Services / Miscellaneous Financial Services BBAS3 Banco do Brasil SA Financial / Financial Intermediaries / Banks BBDC3 Banco Bradesco SA Financial / Financial Intermediaries / Banks BBDC4 Banco Bradesco SA Financial / Financial Intermediaries / Banks BBSE3 BB Seguridade Participações SA Financial / Pension and Insurance / Insurance BEEF3 Minerva SA Non-Cyclical Consumption / Processed Foods / Meat and Meat Products BIDI4 Banco Inter SA Financial / Financial Intermediaries / Banks BPAC11 Banco BTG Pactual SA Financial / Financial Intermediaries / Banks BPAN4 Banco Pan SA Financial / Financial Intermediaries / Banks BRAP4 Bradespar SA Basic Materials / Mining / Metallic Minerals BRDT3 Petrobras Distribuidora SA Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution BRFS3 BRF SA Non-Cyclical Consumption / Processed Foods / Meat and Meat Products BRKM5 Braskem SA Basic Materials / Chemicals / Petrochemicals BRML3 BR Malls Participacções SA Finance / Property Exploration / Property Exploration BTOW3 B2W Cia Digital Cyclical Consumption / Trade / Miscellaneous Products CCRO3 CCR SA Industrial Goods / Transportation / Highway Exploration CESP6 Cesp Public Utility / Electricity / Electricity CIEL3 Cielo SA Financial / Miscellaneous Financial Services / Miscellaneous Financial Services CMIG4 CEMIG Public Utility / Electricity / Electricity CNTO3 Grupo SBF Centauro Cyclical Consumption / Trade / Miscellaneous Products COGN3 Cogna Educação Cyclical Consumption / Miscellaneous / Educational Services CPFE3 CPFL ENERGIA Public Utility / Electricity / Electricity CPLE6 Copel Public Utility / Electricity / Electricity CRFB3 Carrefour BR (Atacadão SA) Non-Cyclical Consumption / Commerce and Distribution / Food CSAN3 Cosan Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution CSMG3 Copasa Public Utility / Water and Sanitation / Water and Sanitation CSNA3 Companhia Siderúrgica Nacional (CSN) Basic Materials / Steel and Metallurgy / Steel CVCB3 CVC Brasil Operadora e Agencia de Viagens SA Cyclical Consumption / Travel and Leisure / Travel and Tourism CYRE3 Cyrela Brazil Realty SA Cyclical Consumption / Civil Construction / Incorporations DTEX3 Duratex SA Basic Materials / Wood and Paper / Wood ECOR3 Ecorodovias Infraestrutura e Logística SA Industrial Goods / Transportation / Highway Exploration EGIE3 Engie Brasil Energia SA Public Utility / Electricity / Electricity ELET3 Eletrobras Public Utility / Electricity / Electricity ELET6 Eletrobras Public Utility / Electricity / Electricity EMBR3 Embraer SA Industrial Goods / Transport Material / Aeronautical and Defense Material ENBR3 EDP Energias do Brasil SA Public Utility / Electricity / Electricity ENEV3 Eneva SA Public Utility / Electricity / Electricity ENGI11 Energisa SA Public Utility / Electricity / Electricity EQTL3 Equatorial Energia SA Public Utility / Electricity / Electricity EZTC3 Eztec Empreendimentos e Participações SA Cyclical Consumption / Civil Construction / Incorporations FLRY3 Fleury SA Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis GGBR4 Gerdau SA Basic Materials / Steel and Metallurgy / Steel GNDI3 Notre Dame Interme´dica Participações SA Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis GOAU4 Metalúrgica Gerdau SA Basic Materials / Steel and Metallurgy / Steel GOLL4 Gol Linhas Aéreas Inteligentes SA Industrial Goods / Transport / Air Transport HAPV3 Hapvida Participações e Investimentos SA Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis HGTX3 CIA Hering Cyclic Consumption / Fabrics, Apparel and Footwear / Apparel HYPE3 Hypera SA Health / Commerce and Distribution / Medicines and Other Products IGTA3 Iguatemi Empresa de Shopping Centers SA Finance / Property Exploration / Property Exploration IRBR3 IRB Brasil Resseguros SA Financial / Pension and Insurance / Insurance ITSA4 Itausa - Investimentos Itaú SA Financial / Financial Intermediaries / Banks ITUB4 Itaú Unibanco Banco Holding SA Financial / Financial Intermediaries / Banks JBSS3 JBS SA Non-Cyclical Consumption / Processed Foods / Meat and Meat Products JHSF3 JHSF Participações SA Cyclical Consumption / Civil Construction / Incorporations KLBN11 Klabin SA Basic Materials / Wood and Paper / Wood Pulp and Paper LAME3 Lojas Americanas SA Cyclical Consumption / Trade / Miscellaneous Products LAME4 Lojas Americanas SA Cyclical Consumption / Trade / Miscellaneous Products LCAM3 Cia de Locação das Américas (LOCAMERICA) Cycle Consumption / Miscellaneous / Car Rental LIGT3 Light SA Public Utility / Electricity / Electricity LINX3 LINX SA Information Technology / Programs and Services / Programs and Services LREN3 Lojas Renner SA Cyclic Consumption / Trade / Fabrics, Apparel and Footwear MDIA3 M Dias Branco SA Industria e Comercio de Alimentos Non-Cyclical Consumption / Processed Foods / Meat and Meat Products MGLU3 Magazine Luiza SA Cyclical Consumption / Commerce / Household Appliances MOVI3 Movida Participações SA Cycle Consumption / Miscellaneous / Car Rental MRFG3 Marfrig Global Foods SA Non-Cyclical Consumption / Processed Foods / Meat and Meat Products MRVE3 MRV Engenharia e Participações SA Cyclical Consumption / Civil Construction / Incorporations MULT3 Multiplan Empreendimentos Imobiliários SA Finance / Property Exploration / Property Exploration NEOE3 Neoenergia SA Public Utility / Electricity / Electricity NTCO3 Natura & Co SA Non-Cyclical Consumption / Personal Use and Cleaning Products / Personal Use Products PCAR3 Pão de Açúcar Companhia Brasileira de Distribuição Non-Cyclical Consumption / Commerce and Distribution / Food PETR3 Petrobras - Petróleo Brasileiro Petrobras SA Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution PETR4 Petrobras - Petróleo Brasileiro Petrobras SA Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution PRIO3 Petrorio SA Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution PSSA3 Porto Seguro SA Financial / Pension and Insurance / Insurance QUAL3 Qualicorp SA Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis RADL3 RAIADROGASIL SA Health / Commerce and Distribution / Medicines and Other Products RAIL3 Rumo S.A. Industrial Goods / Transport / Rail Transport RAPT4 Randon SA Implementos e Participações Industrial Goods / Transport Equipment / Road Equipment RENT3 Localiza Rent a Car SA Cycle Consumption / Miscellaneous / Car Rental SANB11 Banco Santander Brasil SA Financial / Financial Intermediaries / Banks SAPR11 Companhia de Saneamento do Paraná (SANEPAR) Public Utility / Water and Sanitation / Water and Sanitation SBSP3 Cia Saneamento Básico do Estado de São Paulo (SABESP) Public Utility / Water and Sanitation / Water and Sanitation SULA11 Sul Amárica SA Financial / Pension and Insurance / Insurance SUZB3 Suzano S.A. Basic Materials / Wood and Paper / Wood Pulp and Paper TAEE11 Transmissora Aliança de Electricity SA (TAESA) Public Utility / Electricity / Electricity TIMS3 Tim Participações SA Communications / Telecommunications / Telecommunications TOTS3 TOTVS SA Information Technology / Programs and Services / Programs and Services TRPL4 Cia de Transmissão de Electricity Paulista (CTEEP) Public Utility / Electricity / Electricity UGPA3 ULTRAPAR PARTICIPACOES SA Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution USIM5 Usinas Siderúrgicas de Minas Gerais SA (USIMINAS) Basic Materials / Steel and Metallurgy / Steel VALE3 Vale SA Basic Materials / Mining / Metallic Minerals VIVT4 Telefônica Brasil SA Communications / Telecommunications / Telecommunications VVAR3 Via Varejo SA Cyclical Consumption / Commerce / Household Appliances WEGE3 WEG SA Industrial Goods / Machinery and Equipment / Engines, Compressors and Others YDUQ3 YDUQS PARTICIPACOES Cyclical Consumption / Miscellaneous / Educational Services

(1)

(2)

(3)

(4)

(5)

Case	Positive ( θ ⁺ )	Negative ( θ ⁻ )
Before removing the SUZB3 share	0.2926	-0.0775
After removing the SUZB3 share	0.2938	-0.0215

Case	Positive (θ ⁺	Negative (θ ⁻ )
Before removing the SUZB3 share	0.2619	-0.0273
After removing the SUZB3 share	0.2652	-0.0159

Positive (θ ⁺	Negative (θ ⁻ )
0.5735	-

Year	Strength Centrality	Degree Centrality	Eigenvector Centrality
2018	1^st - 41.59	1^st - 78	1^st - 1
2018	93^rd - 7.51	48^th - 0	86^th - 0
2019	1^st - 33.66	1^st - 75	1^st - 1
2019	93^rd - 10.79	50^th - 1	86^th - 0.001
2020	1^st - 62.03	1^st - 80	1^st - 1
2020	94^th - 22.65	50^th - 0	82^nd - 0

Share	Economic Activity	Strength Centrality	Degree Centrality	Eigenvector Centrality
ITUB4	Banks	1^st/41.59	3^rd/75	2^nd/0.999
ITSA4	Banks	2^nd/41.25	3^rd/75	2^nd/0.999
BBDC4	Banks	3^rd/40.79	4^th/74	3^rd/0.994
BBAS3	Banks	4^th/40.25	5^th /73	6^th/0.983
BBDC3	Banks	5^th/39.96	4^th/74	4^th/0.992
SANB11	Banks	6^th/39.79	4^th/74	3^rd/0.994
LAME4	Miscellaneous Products	7^th/38.77	2^nd/76	3^rd/0.994
MULT3	Property Exploration	8^th/38.05	4^th/74	5^th/0.986
B3SA3	Miscellaneous Financial Services	9^th/38	6^th/72	8^th/0.973
LAME3	Miscellaneous Products	10^th/37.19	1^st/78	1^st/1

Share	Economic Activity	Strength Centrality	Degree Centrality	Eigenvector Centrality
MULT3	Property Exploration	1^st/33.66	5^th/70	3^rd/0.981
CYRE3	Incorporations	2^nd/33.25	1^st/75	1^st/1
LREN3	Fabrics, Apparel and Footwear	3^rd/33.22	2^nd/74	2^nd/0.998
CMIG4	Electricity	4^th/33.06	6^th/69	10^th/0.960
BBAS3	Banks	5^th/32.81	4^th/71	11^st/0.958
IGTA3	Property Exploration	6^th/32.47	4^th/71	5^th/0.978
B3SA3	Miscellaneous Financial Services	7^th/32.3	3^rd/73	3^rd/0.981
BRML3	Property Exploration	8^th/31.47	6^th/69	8^th/0.965
RENT3	Car Rental	9^th/31.21	5^th/70	6^th/0.968
LAME4	Miscellaneous Products	10^th/31.07	5^th/70	4^th/0.979

Share	Economic Activity	Strength Centrality	Degree Centrality	Eigenvector Centrality
CYRE3	Incorporations	1^st/62.03	5^st/76	4^st/0.983
BBAS3	Banks	2^nd/61.69	4^th/77	3^st/0.990
UGPA3	Exploration, Refining and Distribution	3^rd/61.08	1^th/80	1^th/1
ECOR3	Highway Exploration	4^th/60.82	2^nd/79	2^rd/0.992
BBDC3	Banks	5^th/60.80	5^th/76	6^th/0.979
CPLE6	Electricity	6^th/60.69	4^th/77	5^th/0.981
BBDC4	Banks	7^th/60.06	6^th/75	9^th/0.972
CMIG4	Electricity	8^th/60.04	6^th/75	11^th/0.965
CSAN3	Exploration, Refining and Distribution	9^th/59.97	3^th/78	7^th/0.977
MOVI3	Car Rental	10^th/59.89	6^rd/75	8^nd/0.975

SHARE	COMPANY NAME	ECONOMIC ACTIVITY
ABEV3	Ambev SA	Non-Cyclical Consumption / Beverages / Beers and Soft Drinks
ALPA4	Alpargatas SA	Cyclic Consumption / Fabrics, Apparel and Footwear / Apparel
ALSO3	Aliansce Sonae Shopping Centers SA	Finance / Property Exploration / Property Exploration
AMAR3	Marisa Lojas SA (LOJAS MARISA)	Cyclic Consumption / Trade / Fabrics, Apparel and Footwear
AZUL4	Azul SA	Industrial Goods / Transport / Air Transport
B3SA3	B3 SA Brasil Bolsa Balcão	Financial / Miscellaneous Financial
		Services / Miscellaneous Financial
		Services
BBAS3	Banco do Brasil SA	Financial / Financial Intermediaries / Banks
BBDC3	Banco Bradesco SA	Financial / Financial Intermediaries / Banks
BBDC4	Banco Bradesco SA	Financial / Financial Intermediaries / Banks
BBSE3	BB Seguridade Participações SA	Financial / Pension and Insurance / Insurance
BEEF3	Minerva SA	Non-Cyclical Consumption / Processed Foods / Meat and Meat Products
BIDI4	Banco Inter SA	Financial / Financial Intermediaries / Banks
BPAC11	Banco BTG Pactual SA	Financial / Financial Intermediaries / Banks
BPAN4	Banco Pan SA	Financial / Financial Intermediaries / Banks
BRAP4	Bradespar SA	Basic Materials / Mining / Metallic Minerals
BRDT3	Petrobras Distribuidora SA	Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution
BRFS3	BRF SA	Non-Cyclical Consumption / Processed Foods / Meat and Meat Products
BRKM5	Braskem SA	Basic Materials / Chemicals / Petrochemicals
BRML3	BR Malls Participacções SA	Finance / Property Exploration / Property Exploration
BTOW3	B2W Cia Digital	Cyclical Consumption / Trade / Miscellaneous Products
CCRO3	CCR SA	Industrial Goods / Transportation / Highway Exploration
CESP6	Cesp	Public Utility / Electricity / Electricity
CIEL3	Cielo SA	Financial / Miscellaneous Financial
		Services / Miscellaneous Financial
		Services
CMIG4	CEMIG	Public Utility / Electricity / Electricity
CNTO3	Grupo SBF Centauro	Cyclical Consumption / Trade / Miscellaneous Products
COGN3	Cogna Educação	Cyclical Consumption / Miscellaneous / Educational Services
CPFE3	CPFL ENERGIA	Public Utility / Electricity / Electricity
CPLE6	Copel	Public Utility / Electricity / Electricity
CRFB3	Carrefour BR (Atacadão SA)	Non-Cyclical Consumption / Commerce and Distribution / Food
CSAN3	Cosan	Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution
CSMG3	Copasa	Public Utility / Water and Sanitation / Water and Sanitation
CSNA3	Companhia Siderúrgica Nacional (CSN)	Basic Materials / Steel and Metallurgy / Steel
CVCB3	CVC Brasil Operadora e Agencia de Viagens SA	Cyclical Consumption / Travel and Leisure / Travel and Tourism
CYRE3	Cyrela Brazil Realty SA	Cyclical Consumption / Civil Construction / Incorporations
DTEX3	Duratex SA	Basic Materials / Wood and Paper / Wood
ECOR3	Ecorodovias Infraestrutura e Logística SA	Industrial Goods / Transportation / Highway Exploration
EGIE3	Engie Brasil Energia SA	Public Utility / Electricity / Electricity
ELET3	Eletrobras	Public Utility / Electricity / Electricity
ELET6	Eletrobras	Public Utility / Electricity / Electricity
EMBR3	Embraer SA	Industrial Goods / Transport Material / Aeronautical and Defense Material
ENBR3	EDP Energias do Brasil SA	Public Utility / Electricity / Electricity
ENEV3	Eneva SA	Public Utility / Electricity / Electricity
ENGI11	Energisa SA	Public Utility / Electricity / Electricity
EQTL3	Equatorial Energia SA	Public Utility / Electricity / Electricity
EZTC3	Eztec Empreendimentos e Participações SA	Cyclical Consumption / Civil Construction / Incorporations
FLRY3	Fleury SA	Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis
GGBR4	Gerdau SA	Basic Materials / Steel and Metallurgy / Steel
GNDI3	Notre Dame Interme´dica Participações SA	Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis
GOAU4	Metalúrgica Gerdau SA	Basic Materials / Steel and Metallurgy / Steel
GOLL4	Gol Linhas Aéreas Inteligentes SA	Industrial Goods / Transport / Air Transport
HAPV3	Hapvida Participações e Investimentos SA	Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis
HGTX3	CIA Hering	Cyclic Consumption / Fabrics, Apparel and Footwear / Apparel
HYPE3	Hypera SA	Health / Commerce and Distribution / Medicines and Other Products
IGTA3	Iguatemi Empresa de Shopping Centers SA	Finance / Property Exploration / Property Exploration
IRBR3	IRB Brasil Resseguros SA	Financial / Pension and Insurance / Insurance
ITSA4	Itausa - Investimentos Itaú SA	Financial / Financial Intermediaries / Banks
ITUB4	Itaú Unibanco Banco Holding SA	Financial / Financial Intermediaries / Banks
JBSS3	JBS SA	Non-Cyclical Consumption / Processed Foods / Meat and Meat Products
JHSF3	JHSF Participações SA	Cyclical Consumption / Civil Construction / Incorporations
KLBN11	Klabin SA	Basic Materials / Wood and Paper / Wood Pulp and Paper
LAME3	Lojas Americanas SA	Cyclical Consumption / Trade / Miscellaneous Products
LAME4	Lojas Americanas SA	Cyclical Consumption / Trade / Miscellaneous Products
LCAM3	Cia de Locação das Américas (LOCAMERICA)	Cycle Consumption / Miscellaneous / Car Rental
LIGT3	Light SA	Public Utility / Electricity / Electricity
LINX3	LINX SA	Information Technology / Programs and Services / Programs and Services
LREN3	Lojas Renner SA	Cyclic Consumption / Trade / Fabrics, Apparel and Footwear
MDIA3	M Dias Branco SA Industria e Comercio de Alimentos	Non-Cyclical Consumption / Processed Foods / Meat and Meat Products
MGLU3	Magazine Luiza SA	Cyclical Consumption / Commerce / Household Appliances
MOVI3	Movida Participações SA	Cycle Consumption / Miscellaneous / Car Rental
MRFG3	Marfrig Global Foods SA	Non-Cyclical Consumption / Processed Foods / Meat and Meat Products
MRVE3	MRV Engenharia e Participações SA	Cyclical Consumption / Civil Construction / Incorporations
MULT3	Multiplan Empreendimentos Imobiliários SA	Finance / Property Exploration / Property Exploration
NEOE3	Neoenergia SA	Public Utility / Electricity / Electricity
NTCO3	Natura & Co SA	Non-Cyclical Consumption / Personal Use and Cleaning Products / Personal Use Products
PCAR3	Pão de Açúcar Companhia Brasileira de Distribuição	Non-Cyclical Consumption / Commerce and Distribution / Food
PETR3	Petrobras - Petróleo Brasileiro Petrobras SA	Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution
PETR4	Petrobras - Petróleo Brasileiro Petrobras SA	Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution
PRIO3	Petrorio SA	Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution
PSSA3	Porto Seguro SA	Financial / Pension and Insurance / Insurance
QUAL3	Qualicorp SA	Health / Hospital Medical Service Analysis and Diagnosis / Hospital Medical Service Analysis and Diagnosis
RADL3	RAIADROGASIL SA	Health / Commerce and Distribution / Medicines and Other Products
RAIL3	Rumo S.A.	Industrial Goods / Transport / Rail Transport
RAPT4	Randon SA Implementos e Participações	Industrial Goods / Transport Equipment / Road Equipment
RENT3	Localiza Rent a Car SA	Cycle Consumption / Miscellaneous / Car Rental
SANB11	Banco Santander Brasil SA	Financial / Financial Intermediaries / Banks
SAPR11	Companhia de Saneamento do Paraná (SANEPAR)	Public Utility / Water and Sanitation / Water and Sanitation
SBSP3	Cia Saneamento Básico do Estado de São Paulo (SABESP)	Public Utility / Water and Sanitation / Water and Sanitation
SULA11	Sul Amárica SA	Financial / Pension and Insurance / Insurance
SUZB3	Suzano S.A.	Basic Materials / Wood and Paper / Wood Pulp and Paper
TAEE11	Transmissora Aliança de Electricity SA (TAESA)	Public Utility / Electricity / Electricity
TIMS3	Tim Participações SA	Communications / Telecommunications / Telecommunications
TOTS3	TOTVS SA	Information Technology / Programs and Services / Programs and Services
TRPL4	Cia de Transmissão de Electricity Paulista (CTEEP)	Public Utility / Electricity / Electricity
UGPA3	ULTRAPAR PARTICIPACOES SA	Petroleum, Gas and Biofuels / Petroleum, Gas and Biofuels / Exploration, Refining and Distribution
USIM5	Usinas Siderúrgicas de Minas Gerais SA (USIMINAS)	Basic Materials / Steel and Metallurgy / Steel
VALE3	Vale SA	Basic Materials / Mining / Metallic Minerals
VIVT4	Telefônica Brasil SA	Communications / Telecommunications / Telecommunications
VVAR3	Via Varejo SA	Cyclical Consumption / Commerce / Household Appliances
WEGE3	WEG SA	Industrial Goods / Machinery and Equipment / Engines, Compressors and Others
YDUQ3	YDUQS PARTICIPACOES	Cyclical Consumption / Miscellaneous / Educational Services

[1] *Corresponding author

Brasil

Brasil

ANALYSIS OF THE BRAZILIAN STOCK MARKET THROUGH GRAPH CENTRALITY MEASURES

ABSTRACT