DIFFUSION PATHS BETWEEN PRODUCT LIFE-CYCLES IN EUROPEAN PHONOGRAPHIC MARKET Andrzej Buda#, Andrzej Jarynowski#* # Institute of Interdisciplinary Research, Wrocław, Poland * Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland We have investigated the product life-cycles of almost 17 000 hit singles performed on the 12 biggest national phonographic markets in Europe including: Austria, Belgium, France, Germany, Ireland, Italy, Netherlands, Norway, Spain, Sweden, Switzerland and the United Kingdom. We have considered weekly singles charts from the last 50 years (1966-2015) in each country. We analyze the spread of hit singles popularity (chart topping) as an epidemiological process performed on various European countries. Popular hit singles are contagious from one country to another. Thus, we consider time delays between the initial hit single release and reaching the highest position on consecutive national singles charts. We create directed network of countries representing transitions of hit singles popularity between countries. It is obtained by simulating the most likely paths and picking up the most frequent links. A country of initial hit single release is considered as a source of infection. Our algorithm builds up spanning trees by attaching new nodes. The probability of attachment depends on: 1) new node's immunity 2) infectivity of previous nodes from the tree. Thus we obtain network of popularity spread with: a hub – the UK, a bridge – the Netherlands and outliers – Italy and Spain. We have found a characteristic topology of hit singles popularity spread. The positive correlation between this network and geographic or cultural grid-map of Europe is also observed. However, the network of popularity spread has some typical properties of complex networks. 1. Introduction Statistical properties of the global phonographic market has been already investigated well by methods of econophysics where the value of an artist has been defined by weekly albums sales. This system is more predictable than financial markets and more complex because of record labels, artists, mass media and additional seasonal groups of collective customers that buy long-playing records. Thus, product life-cycles expressed by trajectories of weekly albums sales reach the maximum in the first week of record sales after the premiere and decrease affected by random processes (Jarynowski and Buda, 2014). However, there is another part of phonographic market represented by songs released as a hit singles. The spread of hit singles popularity over countries reminds classical product life-cycles because the official definition of popularity in case of songs is more complex. National charts have been usually based on weekly physical singles sales, but smaller markets have also compiled official national charts according to official airplays on the radio or TV. On the Internet era (2003 until now), almost all national hit singles charts are mostly based on digital streaming of