Arabidopsis thaliana became the model organism for plant studies because of its small diploid genome, rapid lifecycle and short adult size. Its genome was the first among plants to be sequenced, becoming the reference in plant genomics. However, the Arabidopsis genome is characterized by an inherently complex organization, since it has undergone ancient whole genome duplications, followed by gene reduction, diploidization events and extended rearrangements, which relocated and split up the retained portions. These events, together with probable chromosome reductions, dramatically increased the genome complexity, limiting its role as a reference. The identification of paralogs and single copy genes within a highly duplicated genome is a prerequisite to understand its organization and evolution and to improve its exploitation in comparative genomics. This is still controversial, even in the widely studied Arabidopsis genome. This is also due to the lack of a reference bioinformatics pipeline that could exhaustively identify paralogs and singleton genes. We describe here a complete computational strategy to detect both duplicated and single copy genes in a genome, discussing all the methodological issues that may strongly affect the results, their quality and their reliability. This approach was used to analyze the organization of Arabidopsis nuclear protein coding genes, and besides classifying computationally defined paralogs into networks and single copy genes into different classes, it unraveled further intriguing aspects concerning the genome annotation and the gene relationships in this reference plant species. Since our results may be useful for comparative genomics and genome functional analyses, we organized a dedicated web interface to make them accessible to the scientific community.