Brief Relationship Chart
For reference:
Kyon:
Haruhi: Haruhi, Haruhi-san
Yuki: Nagato, Nagato-san
Mikuru: Asahina, Asahina-san
Itsuki: Koizumi, Itsuki
Summary: Kyon uses Haruhi's first (non-family) name when talking to her, and tacks 'san' on when he's being sarcastic. Yuki and Mikuru have 'san' added until Kyon gets to know them better, but he still tacks on 'san' for Yuki at least one time. (Episode 11) Itsuki is always 'Koizumi,' except in the movie.
Yuki:
Haruhi: Suzumiya Haruhi.
Mikuru: Asahina Mikuru
Kyon: None.
Itsuki: Koizumi Itsuki.
Summary: Yuki, as per her mo, is very clinical/detached when it comes to names, and either avoids addressing a person by their name, or lists their full name.
Haruhi:
Mikuru: Mikuru-chan
Yuki: Yuki
Kyon: Kyon
Itsuki: Koizumi-kun
Summary: Haruhi's very informal with her names, tacking on 'chan' and 'kun' for Mikuru and Itsuki because she thinks they're cute, or something. XD
Mikuru:
Kyon: Kyon-kun
Yuki: Yuki-san (in the movie)
Itsuki: Koizumi-kun, Itsuki-kun
Haruhi: Suzumiya-san
Summary: Mikuru has pretty normal speech forms. What's a little surprising is how formal she is with Haruhi. Well, maybe it's not that surprising.
Itsuki:
Kyon: None (He DOESN'T CALL KYON ANYTHING, I'm surprised. XD)
Yuki: Yuki-san
Haruhi: Suzumiya-san, Your Excellency
Mikuru: None. (Did I miss something? XD;)
Summary: What surprises me most is his lack of reference for Kyon. "Yuki-san" is also taken from the movie.
Other interesting info:
Kyon's sister is the only one to call Yuki: "Yuki-chan."
...But Tsuruya calls her "Nagato Yuki-chan" when they first meet, and later: "Yuki-chi."
Despite their close proximity, the three 'non-human' SOS Brigade members don't talk to each other very much. Apart from the movie, Yuki only talks with Koizumi when they're investigating the cave cricket (and even then, her lines sound more like 'announcements' than specifically to him). The one time Mikuru talks to Yuki is in the 11th episode, about breaking the keyboard, and Yuki doesn't respond.
Furthermore, Koizumi and Mikuru talk to Haruhi quite often, but the only time Yuki and Haruhi really exchange words is in the first and second part of the Island Incident episodes. (When playing: "Who's the king?" and when Haruhi orders Yuki not to open the door, Yuki's one word response is 'Understood.')
Yuki's Canon Relationships:
Suzumiya Haruhi: The key to auto-evolution, Yuki's reason for existence, and her object of observation. The beginning and the end. Yuki regards her as a valid source of authority and follows the (relatively few) orders she receives from her. Other than that, she doesn't seem to have any particular individual feelings about her.
Kyon: Recognizes that Haruhi has 'chosen' him, and therefore he's the key to Suzumiya Haruhi. Also regards him as a valid source of authority to the point she agrees to follow his 'no bogus magic' rule, and his 'I'm rescinding Haruhi's order' tactic in part 2 of the island incident. But even still, Yuki doesn't tell him everything. It's also possible Yuki has some slight feelings for Kyon, because she doesn't rebuild her eyeglasses when Kyon says she looks better without them (and other reasons XD).
Koizumi Itsuki: They have some amount of knowledge about one another, but neither are willing to make the first move to full cooperation. However, there is some subtle acknowledgment here: Yuki never said anything about the murder to anyone else when everyone visits the island, not even Kyon. (And Kyon remarks afterwards: 'She probably knew everything from the start.') Similarly, in the Mysterique Sign episode, Itsuki remarks: "Maybe it was judged this much of my power was necessary." And he gives a short glance to Yuki, implying he at least suspects she's behind the entire thing.
Also interesting to watch is their conversation in the movie about the 'key'. They likely have different goals regarding Haruhi, but are both being ordered by their separate organizations to watch her, so they cooperate.
Asahina Mikuru: Yuki has used Mikuru before (Mysterique Sign), but it's a bit more obvious that their relationship isn't as equal as how Yuki regards Itsuki. Mikuru also seems a bit apprehensive about Yuki to some extent. However, Yuki seems to regard the older Mikuru a little better, as she lets her talk with Kyon privately when she asks.
Kyon's Sister: Yuki doesn't give Kyon's sister the time of day, even when she's poking her asking: "Is that book interesting?" (XD;)
Asakura Ryouko: Had to destroy her. Felt some embarrassment over needing to do it, as evidenced by her comments to Kyon about it being her 'responsibility.' Unknown if they had any real thoughts about each other before Asakura went 'rogue'.
Tsuruya: Yuki ignores her in the baseball episode, but also tells her where Mikuru is in the 'Someday in the Rain' episode, a fact she later concealed from Kyon (though he asked about Haruhi). Thus, Tsuruya is probably little more than a blip on the radar for Yuki.
Kyon:
Haruhi: Haruhi, Haruhi-san
Yuki: Nagato, Nagato-san
Mikuru: Asahina, Asahina-san
Itsuki: Koizumi, Itsuki
Summary: Kyon uses Haruhi's first (non-family) name when talking to her, and tacks 'san' on when he's being sarcastic. Yuki and Mikuru have 'san' added until Kyon gets to know them better, but he still tacks on 'san' for Yuki at least one time. (Episode 11) Itsuki is always 'Koizumi,' except in the movie.
Yuki:
Haruhi: Suzumiya Haruhi.
Mikuru: Asahina Mikuru
Kyon: None.
Itsuki: Koizumi Itsuki.
Summary: Yuki, as per her mo, is very clinical/detached when it comes to names, and either avoids addressing a person by their name, or lists their full name.
Haruhi:
Mikuru: Mikuru-chan
Yuki: Yuki
Kyon: Kyon
Itsuki: Koizumi-kun
Summary: Haruhi's very informal with her names, tacking on 'chan' and 'kun' for Mikuru and Itsuki because she thinks they're cute, or something. XD
Mikuru:
Kyon: Kyon-kun
Yuki: Yuki-san (in the movie)
Itsuki: Koizumi-kun, Itsuki-kun
Haruhi: Suzumiya-san
Summary: Mikuru has pretty normal speech forms. What's a little surprising is how formal she is with Haruhi. Well, maybe it's not that surprising.
Itsuki:
Kyon: None (He DOESN'T CALL KYON ANYTHING, I'm surprised. XD)
Yuki: Yuki-san
Haruhi: Suzumiya-san, Your Excellency
Mikuru: None. (Did I miss something? XD;)
Summary: What surprises me most is his lack of reference for Kyon. "Yuki-san" is also taken from the movie.
Other interesting info:
Kyon's sister is the only one to call Yuki: "Yuki-chan."
...But Tsuruya calls her "Nagato Yuki-chan" when they first meet, and later: "Yuki-chi."
Despite their close proximity, the three 'non-human' SOS Brigade members don't talk to each other very much. Apart from the movie, Yuki only talks with Koizumi when they're investigating the cave cricket (and even then, her lines sound more like 'announcements' than specifically to him). The one time Mikuru talks to Yuki is in the 11th episode, about breaking the keyboard, and Yuki doesn't respond.
Furthermore, Koizumi and Mikuru talk to Haruhi quite often, but the only time Yuki and Haruhi really exchange words is in the first and second part of the Island Incident episodes. (When playing: "Who's the king?" and when Haruhi orders Yuki not to open the door, Yuki's one word response is 'Understood.')
Yuki's Canon Relationships:
Suzumiya Haruhi: The key to auto-evolution, Yuki's reason for existence, and her object of observation. The beginning and the end. Yuki regards her as a valid source of authority and follows the (relatively few) orders she receives from her. Other than that, she doesn't seem to have any particular individual feelings about her.
Kyon: Recognizes that Haruhi has 'chosen' him, and therefore he's the key to Suzumiya Haruhi. Also regards him as a valid source of authority to the point she agrees to follow his 'no bogus magic' rule, and his 'I'm rescinding Haruhi's order' tactic in part 2 of the island incident. But even still, Yuki doesn't tell him everything. It's also possible Yuki has some slight feelings for Kyon, because she doesn't rebuild her eyeglasses when Kyon says she looks better without them (and other reasons XD).
Koizumi Itsuki: They have some amount of knowledge about one another, but neither are willing to make the first move to full cooperation. However, there is some subtle acknowledgment here: Yuki never said anything about the murder to anyone else when everyone visits the island, not even Kyon. (And Kyon remarks afterwards: 'She probably knew everything from the start.') Similarly, in the Mysterique Sign episode, Itsuki remarks: "Maybe it was judged this much of my power was necessary." And he gives a short glance to Yuki, implying he at least suspects she's behind the entire thing.
Also interesting to watch is their conversation in the movie about the 'key'. They likely have different goals regarding Haruhi, but are both being ordered by their separate organizations to watch her, so they cooperate.
Asahina Mikuru: Yuki has used Mikuru before (Mysterique Sign), but it's a bit more obvious that their relationship isn't as equal as how Yuki regards Itsuki. Mikuru also seems a bit apprehensive about Yuki to some extent. However, Yuki seems to regard the older Mikuru a little better, as she lets her talk with Kyon privately when she asks.
Kyon's Sister: Yuki doesn't give Kyon's sister the time of day, even when she's poking her asking: "Is that book interesting?" (XD;)
Asakura Ryouko: Had to destroy her. Felt some embarrassment over needing to do it, as evidenced by her comments to Kyon about it being her 'responsibility.' Unknown if they had any real thoughts about each other before Asakura went 'rogue'.
Tsuruya: Yuki ignores her in the baseball episode, but also tells her where Mikuru is in the 'Someday in the Rain' episode, a fact she later concealed from Kyon (though he asked about Haruhi). Thus, Tsuruya is probably little more than a blip on the radar for Yuki.