Well, at first, they'd probably be very uncomfortable. Snape is used to keeping his thoughts private, and Hermione is a bit shocked by the sudden connection. But as time goes on, they'd become more understanding of each other. Snape would see Hermione's intelligence not as a threat but as an asset, and Hermione would see past Snape's grouchy exterior to the complex person he is.
The mind bond would force them to communicate in a way they never had before. Snape might start to respect Hermione more because he can directly experience her sharp mind and determination. For Hermione, she would get to know Snape's motives better. For instance, she could understand why he was so hard on Harry, which was in part due to his complex relationship with James Potter. This new understanding would lead to a more amicable relationship between them.
Maybe the mind bond is formed during a dangerous magical experiment gone wrong. As a result, Hermione and Snape have to constantly share thoughts and feelings. This forces them to work together despite their initial animosity. Snape might find Hermione's thirst for knowledge and quick thinking surprisingly endearing, and Hermione could see the deep loyalty and hidden kindness in Snape.
In many fanfictions, the soul bond makes Hermione and Draco more empathetic towards each other. For example, in some stories, Draco, who was once a bully, starts to see Hermione's intelligence and kindness in a new light because of the bond. He becomes more protective of her.
Another aspect could be that Hermione sees Snape's past and the hardships he has faced. Maybe she stumbles upon some old memories of his in the library. This newfound understanding makes her more empathetic towards him. As a result, they start to communicate more and form an alliance of sorts, united by their love for Hogwarts and the wizarding world.
It deepens their connection. They become more in tune with each other's feelings. For example, if Harry is in danger, Hermione can sense it more acutely because of the bond.
It makes them closer. The birth bond gives them a sense of loyalty and connection that's deeper than normal friendship. They might trust each other more quickly and be more willing to share secrets.
Well, Hermione is very studious and Sirius is quite rebellious. The soul bond could make Hermione a bit more adventurous. For example, she might be more willing to break some minor rules because she can feel Sirius's disregard for overly strict regulations. And Sirius might become more interested in learning, influenced by Hermione's love for knowledge.
These bonds can also create new relationships. For instance, a Slytherin and a Gryffindor who normally wouldn't interact much might be forced to due to a multi mind bond. At first, they might be hesitant, but over time, they could develop a unique bond that transcends house differences. They might start to see the good in each other and form a strong alliance. This can completely change the social dynamics in Hogwarts. And it could lead to new storylines where characters from different backgrounds work together against common enemies.
At first, their relationship would be full of conflict. Lucius, coming from a pure - blood supremacist background, would likely be disdainful of Hermione, a Muggle - born. However, the soul bond would gradually break down those barriers. They might start to communicate more, with Hermione challenging Lucius' views and Lucius being forced to listen. As time passes, they could develop a mutual understanding, and Lucius might start to see Hermione in a new light, perhaps even becoming protective of her in some situations.
At Grimmauld Place, Hermione and Snape could start off on the wrong foot as usual. But as time passes, they might find common ground. For instance, if they both discover a threat to the wizarding world that is related to Grimmauld Place. Snape's expertise and Hermione's determination could lead them to work together. This shared purpose could make Snape view Hermione as an equal, rather than a student, and Hermione could see Snape's true loyalty and sacrifice, thus changing their relationship for the better.
Their relationship would likely become less antagonistic. Snape has always been tough on Hermione in the original series, but in this fanfiction, as he helps her recover, he would start to see her more as an individual worthy of respect. Hermione, on the other hand, would see Snape's kinder side and perhaps develop a sense of gratitude towards him.