I asked a question about some natural network and after about one hour the question came "On Hold". A similar thing happened here. There is many physicists that work on this area, such as ecology networks, biology networks, finance networks, and models related to them. What is the difference, in terms of being on topic, between questions of interest to physicists who work on a special laser and questions of interest to physicists who work on a special network?
I'm not exactly positive what these network models are, but it sounds like they are a mathematical tool that can be applied to a wide-range of applications (including the ones you listed, and most likely more). I can't say if it is on topic here because, frankly, I don't know enough about it to judge. I will say in response to your comment, though, that just because something is closest to on-topic here and there is no other site available, doesn't mean that it should be allowed here. It's possible that there are questions that are off-topic on every stack exchange site.
I'd also like to point out (and I wish I could find where I've said it before, but I can't at the moment) that just because a topic is of interest to physicists doesn't make it on-topic here. Our scope is questions about physics, not questions by physicists... if a Nobel Prize winner in physics posts a question here about the best apple pie recipe because he/she is interested in cooking, it doesn't mean that it is on-topic. So the focus needs to be on the physics and not just a question a practitioner of physics might have.
Regarding something that seems to have such a broad range of applications, perhaps my suggestion is best revealed by this xkcd comic:
In other words, one could argue that all science is a subset of physics. But physics can be thought of as a subset of math. So perhaps math.SE or math overflow could be better fits, even if you are looking at a physical application? I can't say with any certainty because I don't participate there.
And of course, if you are looking for numerical approaches to these models, scicomp.SE would work. But... I don't know, I don't personally get my hopes up about things there. Our running joke in chat is that unless your question can be answered by "Use petsc," it won't get answered.
tpg2114 makes a good argument on why things used by physicists isn't necessarily physics, so I'm not going to dive in that, but I wanted to put in my perspective on voting to close.
I was originally hesitant about closing the question because network theory is part of statistical mechanics & is studied by physicists. I decided to look up some information about the use of network theory and animal social behaviors (bored while waiting for compiling at work) and posted my findings in two comments on the first link by OP (replicated here in case of deletion and to prevent needing to leave the page):
I will admit that, despite networks being studied by physicists, this doesn't really seem to be physics. Google led me to this book by Croft et al Exploring Animal Social Networks that may be of interest.
The book description in the first comment I made says,
...a practical guide for researchers, undergraduates, and graduate students in ecology, evolutionary biology, animal behavior, and zoology.
while the preprint I linked in the second comment was categorized as Populations and Evolution (q-bio.PE), the q-bio being quantitative biology.
So because neither of these two sources of information were categorized as physics (or some sub-category thereof), I voted to close. It is possible that Biology SE might take this question because of the categorizations of the two resources above, but I am not sure as I'm not active on that site.