A main focus in economics research is understanding the time series of prices of goods and assets. While statistical models using only the properties of the time series itself have been successful in many aspects, we expect to gain a better understanding of the phenomena involved if we can model the underlying system of interacting agents. In this article, we consider the history of Bitcoin, a novel digital currency system, for which the complete list of transactions is available for analysis. Using this dataset, we reconstruct the transaction network between users and analyze changes in the structure of the subgraph induced by the most active users. Our approach is based on the unsupervised identification of important features of the time variation of the network. Applying the widely used method of Principal Component Analysis to the matrix constructed from snapshots of the network at different times, we are able to show how structural changes in the network accompany significant changes in the exchange price of bitcoins.
Despite their relatively low sampling factor, the freely available, randomly sampled status streams of Twitter are very useful sources of geographically embedded social network data. To statistically analyze the information Twitter provides via these streams, we have collected a year's worth of data and built a multi-terabyte relational database from it. The database is designed for fast data loading and to support a wide range of studies focusing on the statistics and geographic features of social networks, as well as on the linguistic analysis of tweets. In this paper we present the method of data collection, the database design, the data loading procedure and special treatment of geo-tagged and multi-lingual data. We also provide some SQL recipes for computing network statistics.
Human interaction networks inferred from country-wide telephone activity recordings were recently used to redraw political maps by projecting their topological partitions into geographical space. The results showed remarkable spatial cohesiveness of the network communities and a significant overlap between the redrawn and the administrative borders. Here we present a similar analysis based on one of the most popular online social networks represented by the ties between more than 5.8 million of its geo-located users. The worldwide coverage of their measured activity allowed us to analyze the large-scale regional subgraphs of entire continents and an extensive set of examples for single countries. We present results for North and South America, Europe and Asia. In our analysis we used the well-established method of modularity clustering after an aggregation of the individual links into a weighted graph connecting equal-area geographical pixels. Our results show fingerprints of both of the opposing forces of dividing local conflicts and of uniting cross-cultural trends of globalization.
As more and more users access social network services from smart devices with GPS receivers, the available amount of geo-tagged information makes repeating classical experiments possible on global scales and with unprecedented precision. Inspired by the original experiments of Milgram, we simulated message routing within a representative sub-graph of the network of Twitter users with about 6 million geo-located nodes and 122 million edges. We picked pairs of users from two distant metropolitan areas and tried to find a route between them using local geographic information only; our method was to forward messages to a friend living closest to the target. We found that the examined network is navigable on large scales, but navigability breaks down at the city scale and the network becomes unnavigable on intra-city distances. This means that messages usually arrived to the close proximity of the target in only 3–6 steps, but only in about 20% of the cases was it possible to find a route all the way to the recipient, in spite of the network being connected. This phenomenon is supported by the distribution of link lengths; on larger scales the distribution behaves approximately as , which was found earlier by Kleinberg to allow efficient navigation, while on smaller scales, a fractal structure becomes apparent. The intra-city correlation dimension of the network was found to be , less than the dimension of the distribution of the population.
Twitter is a popular public conversation platform with world-wide audience and diverse forms of connections between users. In this paper we introduce the concept of aggregated regional Twitter networks in order to characterize communication between geopolitical regions. We present the study of a follower and a mention graph created from an extensive data set collected during the second half of the year of 2012. With a k-shell decomposition the global core-periphery structure is revealed and by means of a modified Regional-SIR model we also consider basic information spreading properties.adapting a simple information propagation model we can further differentiate the most efficient information sources of the world -as reflected in high volume of individual conversations. Methods Twitter dataWe used a data set collected from the freely available Twitter stream during the second half of the year of 2012 [3]. We refer to Twitter users in this data set allowing public access to their geographical location information as the geousers, and each one is located to a single fixed position [3]. Those that fell into unmapped territories (e.g., oceans) were discarded from further analysis. By means of aggregation of their different forms of connections we create two different communication networks between geopolitical regions: the mention (M) and the follower (F ) networks.For creating the user-level follower graph we used 177, 176, 790 links between 3, 312, 961 geo-users identified as the most active ones. Given their list, the additional follower relations were collected separately [3]. The source of a following link is the followed user while its target is the follower. A network built using the inverse follower relation is also be meaningful, and can be used for showing the direction of interest. To create the user-level mention graph we used 132, 436, 279 mention messages between 5, 381, 565 geo-users. The source of a mention link is the sender while its target is the mentioned user.
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