Application of Minimum Vertex Cover Problem in Functional Brain Connectivity Graphs

Brain connectivity networks play a crucial role in understanding the organization and functioning of the human brain. In this regard, graph theoretical models may provide a powerful way for the analysis of brain connectivity networks. The vertex cover (VC) problem, a well-established computational problem in graph theory, may reveal the underlying properties of the brain networks when it is modeled as a graph representation. In the context of brain connectivity, the VC problem aims to identify a minimal set of brain regions that can adequately represent the entire network. To explore the changes in this property by age, a functional magnetic resonance imaging (fMRI) study is conducted with two groups of healthy adults. The characteristics of functional connectivity networks of the young and elderly groups are scrutinized with the minimum vertex cover problem. The results show that in the young participants the vertex cover of brain network includes almost all regions of the brain which indicates that the connections have been distributed homogeneously between the regions so that to cover all edges almost all regions should be added to the minimum VC. However, in the elderly participants the minimum VC sets cover 75% up to 93.75% percent of nodes which indicates in the elderly participants some regions of the brain considerably have more connections than some other parts that can be the sign of weakened connections among some regions.