How important is the choice of a guide/adviser for pursuing PhD in a topic
Working on a PhD in an area where your advisor appears to have little to no expertise in is fraught with danger. A PhD degree is in some sense an apprenticeship - while you need to do the heavy lifting, you also get/need to learn the tricks of the trade from an accomplished master. Every craft has subtler/finer aspects that are not acquired easily. Would you want to rely on someone who himself doesn't appear to know much, even at a high level? I wouldn't do a PhD with such an advisor for the same reasons I wouldn't learn painting from someone who doesn't know it himself/herself. 

On a more important side note, it might not be very wise to jump into a doctorate in an area you have such little knowledge/interest in. You do appear to have the right background, but even with that, doctoral level research in Spectral Graph Theory (and applications, if you are interested in them) is not going to be easy to pick up, even with an expert advisor.