Consider an undirected graph $g$ with some edges having negative weight - all weights in $[-1,1]$. We are seeking communities or clusters. Negative edge weight means repulsion and positive means attraction. Most of the methods I've seen work with positive edges or somehow ignore the negative sign, for example, by rescaling $[-1,1]$ to $[0,2]$ or simply considering absolute value $\|[-1,1]\|$, - etc.
But I cannot ignore the sign. Consider for example a graph with only negative edge weights. If we ignore the negative sign (rescaling, or $\|x\|$, etc.) and use regular methods, then clustering communities will still appear. But by the meaning of repulsion, each node should form its own community in a graph with only negative edge weights, because it cannot cluster with a node that linked to it by an edge with negative weight.
Does anyone know of any method or algorithm that does this?
P.S. This stems from some applied problems, for example, finding communities in groups of people where hate-love relationships are allowed. Note this question was asked IMHO in a less precise formulation and got vague responses. I am still not sure if this is the same as mine, but in any case there are no useful (for me) answers there, and my repulsion seems absent their at all.
