to include first single word in bigram or not? in a text such as 


  "The deal with Canada's Barrick Gold finalised in Toronto over the
  weekend"


When I try to break it into bigram model, I get this

"The deal"
"deal with" 
"with Canada's"
"Canada's Barrick"
"Barrick Gold"
"Gold finalised"
"finalised in"
"in Toronto"
"Toronto over"
"over the"
"the weekend"


my question 

shall I include the first word and the last word as single words

"* The"
"Weekend *"
What you describe is called padding and is indeed used frequently in language modeling. For instance if one represents the sequence "A B C" with trigrams:

# # A
# A B
A B C
B C #
C # #


The advantages of padding:


it makes every word/symbol appear the same number of times whether it appears in the middle of the sequence or not.
it marks the beginning and end of a sentence/text, so that the model can represent the probability to start/end with a particular word.