A nodal region refers to a subgroup (tree) of nodes polarized by an independent node (whose largest flow link connects a smaller node) and a number of subordinate nodes (whose largest flow link connects a larger node). Single or multiple linkage analysis methods are used to reveal such regions by removing secondary links between nodes while keeping only the heaviest links. D and F are independent nodes because their largest flow is directed towards smaller nodes. A, B, C, and E, G are subordinate nodes because their largest flow is directed towards larger nodes (D and F). This algorithm can also be applied to directed graphs and may extend to secondary links (e.g. for each node, including up to 50% of its total traffic) to avoid losing too much information. Such methods are also labeled single linkage analysis (largest flows only) and multiple linkage analysis (largest flows over a certain threshold). They are often used to reveal functional regions based on flow patterns among localities.