Analysis of the Relationship between Mrs Dalloway and Peter Walsh

In the extract taken from the first chapter of the Modernist novel Mrs Dalloway by Virgina Woolf, not only the character of Mrs Dalloway is introduced, but also her relationship with another character, Peter Walsh.
Clarissa reminds a Peter's joke in a morning during her staying at Bourton and her replay. He joked with her, so this underlines they were very close. Mrs Dalloway's answer ("I prefer men to cauliflowers") may be referred to Peter Walsh: she prefers staying with him, a nice man, than with men who have not a personality (cauliflowers is a metaphor).
Mrs Dalloway thinks Peter's letters are very boring, so it is possible to understand she prefers staying personally with him and that his strong personality does not emerges from the letters. Their letters make the reader understand they are still keeping in contact, in spite of the time and the distance between them.
Mrs Dalloway remembers he is coming back from India, but she does not when: he is still important for her but her status of married woman cannot allow her to stay with him and behave with him like when they were young and she was not yet married.
In spite of this, Mrs Dalloway remembers many about Peter: his smile, his eyes and his behaviour make the reader understand she was really interested into him and this features hit her even after many years and her wedding with Mr Dalloway.
So it is possible to think they were close friends or, probably, they were fallen in love with each other, but, if it was, Clarissa married another man, but she keeps still in contact with Peter and she reminds him with many affection.