The directions of an infinite graph G are a tangle-like description of its ends: they are choice functions that choose a component of $G-X$ for all finite vertex sets $X\subseteq V(G)$ in a compatible manner.

Although every direction is induced by a ray, there exist directions of graphs that are not uniquely determined by any countable subset of their choices. We characterise these directions and their countably determined counterparts in terms of star-like substructures or rays of the graph.

Curiously, there exist graphs whose directions are all countably determined but which cannot be distinguished all at once by countably many choices.

We structurally characterise the graphs whose directions can be distinguished all at once by countably many choices, and we structurally characterise the graphs whose directions cannot be distinguished in this manner. Our characterisations are phrased in terms of normal trees and tree-decompositions.

Our four (sub)structural characterisations imply combinatorial characterisations of the four classes of infinite graphs that are defined by the first and second axiom of countability applied to their end spaces: the two classes of graphs whose end spaces are first countable or second countable, respectively, and the complements of these two classes.

无限图G的方向是对其端点的类缠结描述：它们是选择函数，选择$G-X$对于所有有限顶点集$X\subseteq 五(G)$以兼容的方式。

尽管每个方向都是由一条射线诱导的，但存在图的方向不是由它们选择的任何可数子集唯一确定的。我们用星状子结构或图形的射线来表征这些方向及其可数确定的对应物。

奇怪的是，有些图的方向都是可数确定的，但不能通过可数多个选择同时区分。

我们在结构上刻画了可以通过可数多个选择同时区分方向的图，并且我们在结构上刻画了不能以这种方式区分方向的图。我们的特征是用普通树和树分解来表达的。

我们的四个（子）结构表征暗示了四类无限图的组合表征，这些无限图由应用于其末端空间的第一和第二可数公理定义：末端空间分别为第一可数或第二可数的两类图，以及这两个类的补集。