Reddit reviews Networks of Nations: The Evolution, Structure, and Impact of International Networks, 1816-2001 (Structural Analysis in the Social Sciences)
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First of all, social facts of stasis, like high static levels of trade integration, almost certainly do have peaceful consequences. This isn't my dispute.
For the record, though, this is an alternative network study of IR to your Jackson one (though I once took Jackson's online SNA module & it was pretty cool tbh)-- https://www.amazon.com/Networks-Nations-Evolution-International-Structural/dp/0521124573 --and they find either no significant relation between trade integration OR a small positive one. Again, this is a static metric though.
When considered over the long run and, more importantly, dynamic, i.e. rising trade as a component of other globalizing processes, THEN it is related.
Period of rapid or rising trade can be destabilizing and furthermore bring into interaction those who previously did not do so, a sure fire way to increase conflict.
Also, rather than war we should broaden the understanding to 'conflict' generally.
Also, the confounds here are interesting. So we all know the famous result that no two democracies have gone to war, which, in a strict sense, is false, with several violations BUT on the whole it does hold, democracies tend, very strongly, not to fight each other. But a paradox holds: while democracies do not fight each other, they tend to fight authoritarian states more and encourage authoritarian states to fight each other more--in other words, democracies don't fight democracies, but they do increase the rates of global conflict in aggregate. That democracy & trade openness are strongly related in a manner foreclosing a genuine ceteris paribus condition should be obvious & is troubling for both of our arguments.
WWI was at the height of global trade integration of its time--we didn't reach that level again until the 2000s. Furthermore, WWII caused the decline in trade, it was not the result of it.
Also, you oppose protectionism & free trade to each other, even though as absolutes they have never really truly existed. Developed nations always would say they practice free trade, but would not do so in practice, for example.
Also, if you don't consider things like the slave trade, closing of the commons, imperialism & colonialism to be forms of conflict and violence then I don't know what your definition is and those things are definitely correlated to trade integration.