Well, though Hemingway’s story “Old Man at the Bridge” is mainly regarded as a powerful depiction of tragedy of war and how it impacts common people who are ‘without politics’, relationships have also been an important theme here.
 
In the story, we see the old man’s relationship with the animals. He repeats his concern for his pets a number of times while conversing with the narrator. He has no family but the animals — a cat, two goats and four pairs of pigeons. Those are his family. Now, as he is forced to leave the town because of the artillery, his pets are left on their fate. The man expresses his assurance that the cat can look after itself, but he is worried about the other animals. In fact, most part of the conversation is about the animals of the old man. That indicates how powerful the old man’s love is for his animals. 
 
Again, the author mentions the old man’s pleasure and his smile while mentioning his native town San Carlos. That again is about man’s love for his native land. When we are born and brought up at a place, we develop a powerful relationship with that place, with the people living there and the nature around. 
 
So, it won’t be wrong to conclude that Hemingway’s short story “Old Man at the Bridge” focuses on the theme of relationship.