What are genome wide functional linkages?
Genome wide functional linkages refers to protein in a biochemical or signalling pathway. Inferences of functional interactions can be obtained from methods such as coexpression data from microarray analysis. Since experimental detection of genome-wide protein–protein interactions is costly and time-consuming a computational scope for essentially predictive genome-wide protein–protein interactions is created  [1], which is what the above paper is referring to. As obvious from the abstract of the paper, there are many ways of obtaining the linkages, which are often inferred by the Rosetta Stone, Phylogenetic Profile, Operon and Conserved Gene Neighbor computational methods [2]. 

Algorithms that identify genome-wide interactions between proteins mainly focus on coregulation of interacting proteins. These methods assume that the genes that are coregulated often occur close to each other on the genomes and show conserved gene order. Thus the genes, which are part of an operon, could be functionally linked.