Do the Rich Get Richer? An Empirical Analysis of the Bitcoin Transaction Network
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{"title"=>"Do the rich get richer? An empirical analysis of the Bitcoin transaction network", "type"=>"journal", "authors"=>[{"first_name"=>"Dániel", "last_name"=>"Kondor", "scopus_author_id"=>"43661434400"}, {"first_name"=>"Márton", "last_name"=>"Pósfai", "scopus_author_id"=>"26967843600"}, {"first_name"=>"István", "last_name"=>"Csabai", "scopus_author_id"=>"7005508552"}, {"first_name"=>"Gábor", "last_name"=>"Vattay", "scopus_author_id"=>"6701378515"}], "year"=>2014, "source"=>"PLoS ONE", "identifiers"=>{"scopus"=>"2-s2.0-84895544988", "doi"=>"10.1371/journal.pone.0086197", "sgr"=>"84895544988", "arxiv"=>"1308.3892", "isbn"=>"1932-6203", "pmid"=>"24505257", "issn"=>"19326203", "pui"=>"372535259"}, "id"=>"94d13fb7-79f8-3af0-8091-81b0730ea9a2", "abstract"=>"The possibility to analyze everyday monetary transactions is limited by the scarcity of available data, as this kind of information is usually considered highly sensitive. Present econophysics models are usually employed on presumed random networks of interacting agents, and only macroscopic properties (e.g. the resulting wealth distribution) are compared to real-world data. In this paper, we analyze BitCoin, which is a novel digital currency system, where the complete list of transactions is publicly available. Using this dataset, we reconstruct the network of transactions, and extract the time and amount of each payment. We analyze the structure of the transaction network by measuring network characteristics over time, such as the degree distribution, degree correlations and clustering. We find that linear preferential attachment drives the growth of the network. We also study the dynamics taking place on the transaction network, i.e. the flow of money. We measure temporal patterns and the wealth accumulation. Investigating the microscopic statistics of money movement, we find that sublinear preferential attachment governs the evolution of the wealth distribution. We report a scaling relation between the degree and wealth associated to individual nodes.", "link"=>"http://www.mendeley.com/research/rich-richer-empirical-analysis-bitcoin-transaction-network", "reader_count"=>212, "reader_count_by_academic_status"=>{"Unspecified"=>5, "Professor > Associate Professor"=>13, "Researcher"=>27, "Student > Doctoral Student"=>11, "Student > Ph. D. Student"=>56, "Student > Postgraduate"=>12, "Student > Master"=>40, "Other"=>11, "Student > Bachelor"=>24, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>10}, "reader_count_by_user_role"=>{"Unspecified"=>5, "Professor > Associate Professor"=>13, "Researcher"=>27, "Student > Doctoral Student"=>11, "Student > Ph. D. Student"=>56, "Student > Postgraduate"=>12, "Student > Master"=>40, "Other"=>11, "Student > Bachelor"=>24, "Lecturer"=>2, "Lecturer > Senior Lecturer"=>1, "Professor"=>10}, "reader_count_by_subject_area"=>{"Unspecified"=>13, "Agricultural and Biological Sciences"=>9, "Arts and Humanities"=>1, "Business, Management and Accounting"=>29, "Chemistry"=>2, "Computer Science"=>69, "Earth and Planetary Sciences"=>1, "Economics, Econometrics and Finance"=>19, "Engineering"=>9, "Biochemistry, Genetics and Molecular Biology"=>1, "Materials Science"=>1, "Mathematics"=>9, "Medicine and Dentistry"=>2, "Design"=>2, "Physics and Astronomy"=>23, "Social Sciences"=>22}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>2}, "Social Sciences"=>{"Social Sciences"=>22}, "Physics and Astronomy"=>{"Physics and Astronomy"=>23}, "Mathematics"=>{"Mathematics"=>9}, "Unspecified"=>{"Unspecified"=>13}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Design"=>{"Design"=>2}, "Engineering"=>{"Engineering"=>9}, "Chemistry"=>{"Chemistry"=>2}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>19}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>9}, "Computer Science"=>{"Computer Science"=>69}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>29}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}}, "reader_count_by_country"=>{"United States"=>6, "Japan"=>1, "Tanzania"=>1, "Thailand"=>1, "Switzerland"=>2, "India"=>1, "Canada"=>1, "Netherlands"=>1, "Luxembourg"=>1, "Finland"=>1, "Poland"=>1, "Brazil"=>1, "Italy"=>3, "Australia"=>2, "Germany"=>2}, "group_count"=>20}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/1377975"], "description"=>"<p>The cumulative distribution function of the values (see Eq. 5) for exponents and . The inset shows the Kolmogorov-Smirnoff error for these exponents.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks"], "article_id"=>927597, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g007", "stats"=>{"downloads"=>2, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Rank_function_for_new_link_creation_/927597", "title"=>"Rank function for new link creation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377974"], "description"=>"<p>In networks without degree correlations, the degree of connected nodes do not depend on each other, therefore for such networks we expect that is constant. In the case of the Bitcoin network, we observe a clear disassortative behavior: is a decreasing function, indicating that nodes with high outdegree tend to connect to nodes with low indegree.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "indegree", "neighbors", "outdegree"], "article_id"=>927596, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g006", "stats"=>{"downloads"=>0, "page_views"=>21, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_average_indegree_of_neighbors_in_the_function_of_the_outdegree_/927596", "title"=>"The average indegree of neighbors in the function of the outdegree .", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377970"], "description"=>"<p>The black line shows a fitted power-law for the final network; the exponent is . The data is log-binned for ease of visual inspection, the power-law is fitted on the original data <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086197#pone.0086197-Clauset1\" target=\"_blank\">[18]</a>.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "outdegree"], "article_id"=>927593, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g003", "stats"=>{"downloads"=>0, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_outdegree_distribution_/927593", "title"=>"Evolution of the outdegree distribution.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377969"], "description"=>"<p>Since the beginning of 2011, the shape of the distribution does not change significantly. The black line shows a fitted power-law for the final network; the exponent is . The data is log-binned for ease of visual inspection, the power-law is fitted on the original data <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086197#pone.0086197-Clauset1\" target=\"_blank\">[18]</a>.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "indegree"], "article_id"=>927591, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g002", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_indegree_distribution_/927591", "title"=>"Evolution of the indegree distribution.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377983"], "description"=>"<p>We calculate the averages for logarithmically sized bins. We find strong correlation between the balance and the indegree of individual nodes. The main plot shows indegree values up to , only 75 nodes () have higher indegree, the averages calculated for such small sample result in high fluctuations (see inset). We also measure both the Pearson and Spearman correlation coefficient: The Pearson correlation coefficient of the full dataset is , while the Spearman rank correlation coefficient is . (Note that the Pearson correlation coefficient measures the linear dependence between two variables, while the Spearman coefficient evaluates monotonicity). We test the statistical significance of the correlation by randomizing the dataset 1000 times and calculating the Spearman coefficient for each randomization. We find that the average Spearman coefficient is with a standard deviation of , indicating that the correlation is indeed significant.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "node", "balances"], "article_id"=>927605, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g012", "stats"=>{"downloads"=>2, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_node_balances_as_a_function_of_the_indegrees_/927605", "title"=>"Average node balances as a function of the indegrees.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377968"], "description"=>"<p>Number of addresses with nonzero balance (green), addresses in participating in at least one transaction in one week intervals (red) and the exchange price of bitcoins in US dollars according to MtGox, the largest Bitcoin exchange site (blue). The black lines are exponential functions bounding the growth of the network size; the characteristic times are and days.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "bitcoin"], "article_id"=>927590, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g001", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_growth_of_the_Bitcoin_network_/927590", "title"=>"The growth of the Bitcoin network.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377982"], "description"=>"<p>The cumulative distribution function of the values (see Eq. 5) for exponents , , , , , , and . The inset shows the maximum Kolmogorov-Smirnoff error for these exponents. Here, the results are not as obvious as in the case of link creation (Fig. 7; a simple power-law form like in Eq. 4 is not sufficient to accurately model the statistics of money flow. On the other hand, the “average” behavior shows a correlation between the balance and the increase of the balance: the uncorrelated assumption () clearly gives a much worse approximate than the exponents that presume preferential attachment ().</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks"], "article_id"=>927604, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g011", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Rank_function_for_the_growth_of_balances_/927604", "title"=>"Rank function for the growth of balances.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377978"], "description"=>"<p>The distributions are shifted by arbitrary factors along the vertical axis for better visibility of the separate lines. The black lines are stretched exponential and power-law fits of the last empirical distribution. The tail can be approximated by a power-law with exponent , however, the rest of the fit is unsatisfactory. Therefore, we fit the distribution with a stretched exponential distribution of form . We find a better approximation of the whole distributions; the parameters are and .</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "balances", "bitcoin"], "article_id"=>927600, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g009", "stats"=>{"downloads"=>0, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_distribution_of_balances_of_individual_Bitcoin_addresses_/927600", "title"=>"Evolution of the distribution of balances of individual Bitcoin addresses.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377976"], "description"=>"<p>We observe a power-law distribution close to the widely observed , the exponential cutoff corresponds to the finite lifetime of the Bitcoin system.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "transactions", "initiated", "bitcoin"], "article_id"=>927598, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g008", "stats"=>{"downloads"=>1, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Distribution_of_time_delay_between_transactions_initiated_from_a_single_Bitcoin_address_/927598", "title"=>"Distribution of time delay between transactions initiated from a single Bitcoin address.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377973"], "description"=>"<p>After the initial phase, both measures reach a stationary value.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "clustering", "coefficient", "out-in"], "article_id"=>927595, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g005", "stats"=>{"downloads"=>3, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_clustering_coefficient_and_the_out_in_degree_correlation_coefficient_/927595", "title"=>"Evolution of the clustering coefficient and the out-in degree correlation coefficient.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377972"], "description"=>"<p>We observe the distinct initial phase lasting until mid-2011. The trading phase is characterized by approximately constant coefficients.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "gini", "coefficient"], "article_id"=>927594, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g004", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_of_the_Gini_coefficient_of_the_degree_and_the_balance_distributions_/927594", "title"=>"Evolution of the Gini coefficient of the degree and the balance distributions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377985"], "description"=>"<p>Here we have four input (I–I) and three output (O–O) addresses. Links in our analysis are created pointing from each input to each output address.</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "bitcoin"], "article_id"=>927607, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g013", "stats"=>{"downloads"=>6, "page_views"=>45, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_view_of_a_Bitcoin_transaction_/927607", "title"=>"Schematic view of a Bitcoin transaction.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/1377981"], "description"=>"<p>Increase (top) and decrease (bottom, vertical axis is inverted) of node balances in one month windows as a function of their balance at the beginning of each month. We show the raw data (red), the average (green), median (blue) and logarithmic average (magenta). The later three are calculated for logarithmically sized bins. We find a clear positive correlation: addresses with high balance typically increase their wealth more than addresses with low balance. The median and the logarithmic average values almost coincide, which suggests multiplicative fluctuations. The median and the logarithmic average increase approximately as power-laws for several orders of magnitude. The black line is a power-law fit for the double logarithmic data; the exponent is .</p>", "links"=>[], "tags"=>["Information technology", "databases", "statistics", "Statistical methods", "Interdisciplinary physics", "Statistical mechanics", "Economics", "Mathematical economics", "Sociology", "social networks", "balances"], "article_id"=>927603, "categories"=>["Physics", "Mathematics", "Sociology"], "users"=>["Dániel Kondor", "Márton Pósfai", "István Csabai", "Gábor Vattay"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0086197.g010", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Change_of_balances_in_one_month_windows_/927603", "title"=>"Change of balances in one month windows.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2014-02-05 03:56:31"}

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Relative Metric

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