The theme of relationship revolves around Sophy's relationships: Sophy and Sam Hobson; Sophy and Vicar Twycott; Sophy and Randolph. A secondary but influential relationship is that inferred between Randolph and his father, the Vicar Twycott. In a subtle examination of these four relationships, Hardy represents beneficial relationships and harmful relationships.
From what we know of Sam Hobson, in his love for her, he had always put Sophy's happiness and welfare before his own. For instance, when she was nineteen, he asked her if she would be his wife but only when he could provide a home for her:
"You see, dear Sophy, ... you may want a home; and I shall be ready to offer one some day, though I may not be ready just yet."
Another instance is when they became reacquainted after Twycott's death and Sam encouraged Sophy to ride out with him in the clean air of the morning as he delivered produce to Covent Garden. This and subsequent excursions in the pre-dawn hours gave her renewed strength and permitted her better sleep than the sleepless nights that followed an invalid's days without exercise.
"Now, wouldn't some air do you good? ... Why not ride up to Covent Garden with me?" ... The air was fresh as country air at this hour, and the stars shone, ... "There is no time o' day for taking the air like this."... The air and Sam's presence had revived her: her cheeks were quite pink--almost beautiful.
Twycott also had put Sophy's welfare before his own. He had fallen in love with her quiet presence and tender ways and his affection was strengthened by his duty to provide some relief for her after being the unintentional cause of her fall and permanent ankle injury. In marrying her, he provided for her future as well as for his own, and he moved his new bride to a prestigious parish "south of London" where her social inferiority would be less keenly felt by both.
The harmful relationship between Sophy and her son--which seems to grow out of his devoted relationship to his father, who must have shone compared to rough-bred Sophy--contrasts to these first two relationships by being centered on his father's and his own welfare, without thought given to Sophy's benefit or happiness. It may be inferred that Twycott did not defend Sophy before Randolph for fear that her influence in speech and manner might interfere with his future as a gentleman of first rank. Indeed, the seed of this social self-consciousness was present in his move to London:
Mr. Twycott knew perfectly well that he had committed social suicide ... and he had taken his measures accordingly. An exchange of livings had been arranged with ... a church in the south of London, ....
This examination of the theme of relationship seems to suggest that Hardy is identifying selfishness as the seed that tells beneficial relationships from harmful ones. Sam showed no selfishness, even selflessly waiting for her all those years between reencountering Sophy and her funeral. Twycott showed no selfishness in his desires at the start but his consciousness of "social suicide" revealed a blossoming selfishness at the heart of his motivations. Randolph demonstrated full blown selfishness from the start and his was the relationship that did Sophy harm.
"'Has,' dear mother--not 'have'!" exclaimed the public-school boy, ... "Surely you know that by this time!" [...] "I am ashamed of you! It will ruin me! ... It will degrade me in the eyes of all the gentlemen of England!"
the theme is about sacrafice and love which sophy gave to her son and about creulty which was given to her by her husband and son sry my english is not that good