A member of the Vanguard Unionist Progressive Party in the 1970s, he, along with David Trimble, moved into the Ulster Unionist Party, and as head of the youth wing, he was critical of both the British government's perceived indecisiveness and (more quietly) the UUP leadership under James Molyneaux
In a communique taking responsibility for the killing, the IRA command said his killing should be a salutary lesson to those loyalists who stand foursquare behind the laws and forces of oppression of the nationalist people. IRA members said that Graham was targeted because of aid and advice he had reportedly given to the Northern Ireland Prison Service
After Graham's killing, an expression of sympathy was made by the Seanad Éireann
I would like the Seanad to note with horror and dismay the death of the Assembly man, Edgar Graham, who was murdered outside Queen's University, Belfast, this morning. It has been said by a noted writer that in the death of every man each of us dies a little. I think this is horribly true for us here in Ireland today that for every one of these victims of violence not only do we die a little but our hopes for our country die a little with every one of these outrages.The resultant Assembly by-election on 1 March 1984 was won unopposed by then Ulster Unionist Party Chief Executive Frank Millar Jr.
The UUP leader, Lord Molyneaux remarked
"Had Mr. Graham not been murdered he would have become the leader of our party, such was his caliber."
In honour and remembrance to Edgar Graham there is a inscription at the entrance of the debating hall at Stormont that reads:
"IN MEMORY OF EDGAR SAMUEL DAVID GRAHAM ASSEMBLY MEMBER FOR BELFAST SOUTH 1982-1983. SHOT BY TERRORISTS ON 7 DECEMBER 1983. 'KEEP ALIVE THE LIGHT OF JUSTICE'.
Some had been targeted by republicans because of their involvement in Unionist politics. Many knew Robert Bradford and Edgar Graham both murdered for defending the Union. Despite this they were prepared to share power with Sinn Féin. This displayed a magnanimity, and generosity of spirit which unfortunately has not yet been reciprocated by republicans. When we ‘jumped first’ and established the devolved Executive last November, the IRA just sat on its guns and did nothing with the result that the British Government had to suspend the Executive.
"Queens University is today a very different place than it was in the mid 80s when I matriculated. At the height of the troubles, post the hunger strikes and shortly after the murder of Edgar Graham not far from this hall. It was for many Protestants an inhospitable place ... [H]e would honour the memory of men like Sir Norman Stronge, his son James, Councillor Charlie Armstrong, the Reverend Robert Bradford, Senator John Barnhill, and Edgar Graham who were killed by thugs under the guise of a perverted political philosophy ... [T]he RUC officer who trained Edgar Graham in the use of a personal firearm, just weeks before his untimely murder, told me that he would not have known what hit him, for it happened so quickly and was done from behind, in a cowardly fashion. Members here today know what hit Edgar Graham, and who organised the attack. I sat this morning, with my head bowed, as we witnessed an attempt by Her Majesty's Government to place in positions of power those who signed Mr Graham's death warrant. Those who, this morning, were put forward for positions in the Government of Northern Ireland have been responsible for terrorising the very community over which they were to exercise authority."
"It is also puzzling for Unionists why Sinn Féin/IRA are campaigning so vigorously to defend the reputation of Mr Finucane as that of a "human rights lawyer" whilst justifying their murder of the Protestant Human Rights Lawyer, Mr Edgar Graham at Queen's University."
"The most predictable unionist reaction focuses on the demand that more attention be paid to those murdered by the IRA over the years such as law lecturer Edgar Graham and members of the judiciary including Judges Conaghan, Doyle and Gibson (and his wife), and Resident Magistrates Staunton, Mc Birney and the daughter of a Resident Magistrate, Mary Travers, killed during an attack on her father. Why, it is argued, are there no demands for international independent inquiries in these and other cases? Why the focus on Pat Finucane and Rosemary Nelson? The argument completely misses the point. There are no allegations that members of the security forces routinely issued death threats, demonised, had prior knowledge of or colluded in any way in these murders. There is no suggestion that the security forces were less than thorough in the subsequent investigations. At times it is necessary to state the obvious."
David Trimble has invoked his friend's killing to show both that the Unionist community had suffered greatly at the hands of republicans, and that more moderate Unionists were willing to take bold moves (especially support for the Good Friday Agreement) and were willing put their suffering behind them.
Journalist Ed Moloney, in his 2003 book, "A Secret History of the IRA", contends that Graham's killing was ordered by a restive IRA unit, the Belfast Brigade and Ivor Bell, as part of a campaign that was a direct challenge to Sinn Féin leader Gerry Adams' call for a more "controlled and disciplined" campaign twined with a growing parliamentary strategy. Moloney argues that Belfast area attacks by the IRA in late 1983, because of their backlash in the middle classes of both communities, in fact strengthened Adams and Sinn Féin's political path.
Ironically, despite Graham's murder, violence in Northern Ireland actually continued in a pattern of decline in 1983, with 77 deaths, down from 97 the previous year. The British Army suffered only five deaths in 1983, its lowest number since 1971, while combined secutity services suffered 33 deaths (a drop from 40 the year before), and civilian deaths were recorded as 44, the lowest number since 1970.