• algorithms
• social networks
• theory graph

The aim of the present work has been to provide a social investigation for three operators based on their CDRs (Call Data Records), to discover basic properties and the Strongly Connected Components inside our directed graph.
After the use of a specific program for social analysis, named NetworkX, we moved our attention to implement by ourselves a better and faster solution to build a Directed Graph and run on it some algorithms.
For basic properties we obtained really good results in terms of speed and memory occupation, instead of all other programs, that could find more properties, but slower and with a non optimization filling of the RAM memory.
After few days of phone/VoIP traffic, we discovered inside all the three networks the presence of a big group, that we called the Biggest Strongly Connected Component (SCC). This behavior reflects exactly the portion of the users that have both, fan-in and fan-out in those days, in the respect of mathematical definition. The remaining parts of the networks are composed by Single Islands, with just one user inside, or really Small Islands, with few users inside.
In conclusion, we were able to analyze for first a real and huge CDR and with the use of graph’s theory and of our specific directed graph, we found some basic and advanced network characteristics, like the strongly connected components.
The thesis is enriched by numerous images and tables obtained from the test results, in order to clarify to the reader the main steps executed.