Diffusion paths between product life-cycles in European phonographic   markets
  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 nodes 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. 
Andrzej Buda, Andrzej Jarynowski
physics.soc-ph cs.SI nlin.AO stat.AP