i agree with the above poster, it CAN be a sign of nutrient deficiency but usually its just a trait. its generally NOT a sign of nute deficiency, ive had plants and clones both having purple petioles (stem on leaf), sometimes theyll get purple streaks on the stem but its not a deficiency - i feed my babies 5 bottles of various researched & proven to be quality nutes and they always grow beautifully. this has been the case for a few different strains, side by side grows of mine and my buddy shows purple stems being a trait. on another note, im sure certain deficiencies result in purple stems, such as the need for transplanting. since your stems are VERY purple, you prolly need to transplant. generally, the leaves will get smaller and the plant will eventually get stunted.
in my plant biology class, purple stem / green leaves were generic traits that we crossed and bred. the purple on the "fast plants" that we used looked very similar to the purple on the petioles/stems of weed. also, low temps can cause this - if its 80 for day and 65 at night then your bud will purp up. also, its not necessarily a sign of nitrogen deficiency as someone stated above - nitrogen deficiencies result in yellowing leaves, dunno bout purp stems too since its so common.
id really like an indepth scientific answer to this, like how to differentiate between purple as a deficiency and purple as a trait - but like i said, typically a deficiency for transplanting will be accompanied by smaller leaves and stunted growth.