Some more specifics:
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Network autocorrelation can, if strong enough, cause arbitrarily large changes in both the direction of effects, and the significance levels.
You should be able to explore this via simulation. For example:
x <- discrep_net_prop_more.W
y <- BLQFMHEDWM.W
fit <- lm(y ~ x)
lambda <- 0
y_sim <- fit$coefficients%*%cbind(1,x) + Solve(diag(1, length(x)) - lambda* w.list.trunc)) %*% rnorm(length(x), 0, summary(fit)$sigma)
summary(fit_sim <- lm(y_sim ~ x))
(w.list.trunc is an n x n matrix, right?)
For lambda = 0, there should be no significant differences between fit_sim and fit. However, as you change lambda (making it larger in magnitude, both positive and negative), you can see how the results of the linear model will change from network autocorrelation.
What the network autocorrelation model does is fit this extra "lambda" parameter that is the strength of the network autocorrelation, and this "subtracts out" the effect of the network autocorrelation thereby "leaving behind" only the "pure" effect of the explanatory variables on the response variable (ideally).
(Note that conceptually, for the simulation you should probably be using the fitted network autocorrelation model---as it has "subtracted out" existing network autocorrelation--rather than the fitted linear model which still has the network autocorrelation present, but just to understand what network autocorrelation can do in general, it's not really relevant what data you use since the original fitted model can act as your "truth" for referencing back to. If you're interested in how network autocorrelation may be acting in your specific data, then use the coefficients and estimated sigma from spautolm instead of lm(y~x).)
You can also see how different network autocorrelation structure would change the results by putting in different weights matrices.
But of course, every model comes with assumptions. Network autocorrelation models assume (1) the effect of network autocorrelation is constant throughout the network, and (2) you are using the correct weights matrix to measure potential network autocorrelation (the correct choice is not necessarily obvious! See Leenders 2002, "Modeling social influence through network autocorrelation: constructing the weight matrix"). Personally, these assumptions are a bit too heavy for my taste, but additionally, network autocorrelation models can only (at best) control for all network dependencies at once; they cannot substantively describe (estimate and perform inference on) specific dependencies, which is what most network modeling is concerned with.
If you want to continue with a network autocorrelation approach, George's suggestion of looking into spatial econometrics is an excellent one. The weights matrix for network autocorrelation attempts to capture network dependencies rather than spatial ones, but otherwise, the modeling process is very similar and there is a lot more work with spatial errors and types of spatial regression models. Luc Anselin's work, in particular, has some great exemplars of spatial regression in practice.