This is a page under development (by Reza Naserasr) to help with development of the theory of signed graphs.
One of the main difficulties in working on signed graphs is that there competing terminologies even for the most basic notions. For example, while some authors consider edges of a signed graph to be either positive or negative, hence working with the multiplicative group \( (\{+,-\}, \times) \), some others rather use the classic additive group \( \mathbb{Z}_2 \) in which case edges are odd or even.
One of the basic problems caused by this particular difference of views is as follows: authors using multiplicative group commonly take all positive signs as natural way of viewing classic graphs as special case of signed graphs. But authors using additive group, viewing an edge as distance 1, assign 1 to all edges in order to view a graph as special case of signed graph. However, in the correspondence between multiplicative and additive groups on two elements, 1 matches -.
To compromise, for this particular difference of terminology, we work with + and - as signs of the edges, but to view a graph as special case of signed we take all edges to be negative.
We hope that this website will help with merging of the notions and terminologies in long term.
We also wish to have a source for most motivating research questions on the subject with regular updates on progress.
Your help and contribution would be essential to reach that goal. That can vary from simply mentioning your preferred terminologies to proposing concepts, specific signed graphs and open problems to be added.