Linearly bounded Turing machines have been mainly studied as acceptors for context-sensitive languages. We define a natural family of canonical infinite automata representing their observable computational behavior, called linearly bounded graphs. These automata naturally accept the same languages as the linearly bounded machines defining them. We present some of their structural properties as well as alternative characterizations in terms of rewriting systems and context-sensitive transductions. Finally, we compare these graphs to rational graphs, which are another family of automata accepting the context-sensitive languages, and prove that in the bounded-degree case, rational graphs are a strict sub-family of linearly bounded graphs.