Graph/Network building and analysis of linked polygons in ArcGIS 10.2

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This is more of a follow-up question to Divide polygons into *n* number of groups of equal counts with ArcGIS 10.2 and grouping village points based on distance and population size, particularly the answers by FelixIP.

I am trying to group a set of polygons spatially with a max population constraint. (The Grouping Analysis tool in ArcGIS is similar to desired results, but can only do temporal or spatial constraints, no population -- so some network analysis with ArcPy is needed.)

I am mostly following the steps outlined in FelixIP's answer in the first question, but am stuck at the part where he suggests "[fi] and [ti] are sequential number of connected nodes. To populate this table search this forum on how to assign from and to nodes to link." Unfortunately, there seems to be no such answer (or I'm phrasing poorly), hence my question:

How do I create a network/graph that can be used to calculate the number of sequentially connected nodes? And in fact, do I correctly understand that these [fi] and [ti] fields represent the total number of nodes that each node can be reached from (fi) and the number of neighbor nodes each node can reach (ti)?

So far I have everything else needed until that point: a Point node layer, and a Polyline link layer (with from and to node). Visual aid below for context:





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