Mr. Graham practises almost exclusively in High Court and he estimates having been instructed in more than 1,200 High Court indictments, and having conducted in excess of 350 High Court trials.
He is regarded as "Senior Junior" Counsel and often leads Junior Counsel. He is instructed to defend the most serious of charges, and has been instructed as leader in more than 30 murder trials.
Mr. Graham regularly appears in the Appeal Court, has appeared before the Judicial Committee of the Privy Council, the Judicial Committee of the General assembly of The Church of Scotland, and Fatal Accident Inquiries.
As an ad hoc Advocate Depute he has prosecuted crimes involving significant violence, sexual offences, robbery, firearms offences, and drugs
In relation to media law, Mr. Graham has been instructed over many years by national newspapers and press agencies providing pre publication advice. He has an interest in medicine, engineering and science.