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Temporal Statistical Analysis of Degree Distributions in an Undirected Landline Phone Call Network Graph Series

Department of Mathematics, University Ismail Qemali, Str. Kosova, 9400 Vlore, Albania
Received: 26 July 2017 / Revised: 3 October 2017 / Accepted: 6 October 2017 / Published: 9 October 2017
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Abstract

This article aims to provide new results about the intraday degree sequence distribution considering phone call network graph evolution in time. More specifically, it tackles the following problem. Given a large amount of landline phone call data records, what is the best way to summarize the distinct number of calling partners per client per day? In order to answer this question, a series of undirected phone call network graphs is constructed based on data from a local telecommunication source in Albania. All network graphs of the series are simplified. Further, a longitudinal temporal study is made on this network graphs series related to the degree distributions. Power law and log-normal distribution fittings on the degree sequence are compared on each of the network graphs of the series. The maximum likelihood method is used to estimate the parameters of the distributions, and a Kolmogorov–Smirnov test associated with a p-value is used to define the plausible models. A direct distribution comparison is made through a Vuong test in the case that both distributions are plausible. Another goal was to describe the parameters’ distributions’ shape. A Shapiro-Wilk test is used to test the normality of the data, and measures of shape are used to define the distributions’ shape. Study findings suggested that log-normal distribution models better the intraday degree sequence data of the network graphs. It is not possible to say that the distributions of log-normal parameters are normal. View Full-Text
Keywords: longitudinal; degree distribution; network graph; phone call data; power law; log-normal longitudinal; degree distribution; network graph; phone call data; power law; log-normal
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Gjermëni, O. Temporal Statistical Analysis of Degree Distributions in an Undirected Landline Phone Call Network Graph Series. Data 2017, 2, 33.

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