Nerva had rumors recorded about him having affairs with men, and was a lifelong bachelor which was EXTREMELY unusual even for Romans who preferred men.

Now, Trajan? He was well-known for preferring male company.

Trajan was most conspicuous for his justice, for his bravery, and for the simplicity of his habits. He was strong in body, being in his forty-second year when he began to rule, so that in every enterprise he toiled almost as much as the others; and his mental powers were at their highest, so that he had neither the recklessness of youth nor the sluggishness of old age. He did not envy nor slay any one, but honoured and exalted all good men without exception, and hence he neither feared nor hated any one of them. To slanders he paid very little heed and he was no slave of anger. He refrained equally from the money of others and from unjust murders. He expended vast sums on wars and vast sums on works of peace; and while making very many urgently needed repairs to roads and harbours and public buildings, he drained no one’s blood for any of these undertakings. He was so high-minded and generous that, after enlarging and embellishing the Circus, which had crumbled away in places, he merely inscribed on it a statement that he had made it adequate for the Roman people.

For these deeds, now, he took more pleasure in being loved than in being honoured. His association with the people was marked by affability and his intercourse with the senate by dignity, so that he was loved by all and dreaded by none save the enemy. He joined others in the chase and in banquets, as well as in their labours and plans and jests. Often he would take three others into his carriage, and he would enter the houses of citizens, sometimes even without a guard, and enjoy himself there. Education in the strict sense he lacked, when it came to speaking, but its substance he both knew and applied; and there was no quality which he did not possess in a high degree.

I know, of course, that he was devoted to boys and to wine, but if he had ever committed or endured any base or wicked deed as the result of this, he would have incurred censure; as it was, however, he drank all the wine he wanted, yet remained sober, and in his relation with boys he harmed no one. And even if he did delight in war, nevertheless he was satisfied when success had been achieved, a most bitter foe overthrown and his countrymen exalted. Nor did the result which usually occurs in such circumstances — conceit and arrogance on the part of the soldiers — ever manifest itself during his reign; with such a firm hand did he rule them.

• Cassius Dio