I understand the basis of graph theory as it applies to trade route detection, but simply because the algorithm to detect the longest path is correct and optimal, it doesn't mean this is the way things should work in game.
The basic premise behind trade in economics is that it creates efficiency.. i.e. it is more efficient for some people in location X to create resource x and trade with the people in location Y for resource y than it is for the people at location X to create both x and y. Basically, when you increase trade capacity, you are "creating" wealth by allowing more optimization of resource production. This also means you are creating more resources per amount of work. In essence, any time you ease trade restrictions (whether it is by changing a law or inventing the rail road), the amount of value gained per amount of work for the system increases. It has nothing to do with the longest trade route.. this is a myth possibly originating with the silk road.
Distance does factor into trade in one way. It increases the cost of trade. If X and Y are very far apart, it might cost more to transport resources between the two than it would for each to produce both x and y themselves. In addition, if x can only be produced at X and y can only be produced at Y (rare resources), then the cost of buying resource x at location Y is high.. and thus more taxable. Thus, the illusion of greater profits from trade over distance. The reality is that adding more efficiency to the system may mean lower sale prices and lower tax income per unit of resource, but it also means a much greater volume of resource is traded.. net tax revenue will increase.
For Sins, all this means is that the trade network system currently makes no sense. Example: you have a network of planets connected by trade routes a-b-c-d-e. As was used in the example posted earlier, d is currently 3 jumps from a. If you then connect e to a giving you a-b-c-d-e-a, d is only 2 jumps from a. In SINS, this means your tax revenue from trade decreases. In reality, this situation would mean the cost of transporting goods from a to d would decrease, meaning an increase in volume of goods transported and an increase in the number and size of competitive traders vying for the market. The increased efficiency of the new route means more people are getting more of what they want than they could before at lower prices than they could before. No matter how you look at it, this increases the net value of the entire system, including the amount of tax the government should be recieving. SINS method is flawed.
The only time that increasing efficiency of a trade network would not result in an increase in income would be if resource production was already maxed out. Without the ability to produce more of x, creating a situation that reduces the cost of transporting x will be offset by the laws of supply and demand.. forcing the price to remain high because supply can't increase. This is far more complex than the SINS economic situation though and can safely be ignored. In any case, it does not result in a loss of tax revenue.
(side note) Those of you who argue for protectionist trade policy have a point.. namely it is possible for one element within a trade network to be operating at a net loss compared to another. The system as a whole always becomes more efficient when trade restrictions are lifted, but certain elements within the network may be less well off than before. This is also well outside the realm of SINS, unless the new expansion takes into account inter-empire trade in a more meaningful way