Trust statements are weighted, in the sense that the source user can express how much she trust the target user on a numerical scale, usually and by convention this value is mapped in the range [0,1], where 0 means distrust and 1 means total trust.
Trust statements are subjective, every user is free to express a different trust level on each users. For example, in the figure above, Alice is free to express trust in Carol as 0.1 (very low trust) and Bob is free to express trust in Carol as 0.95 (very high trust). Both trust statements are equally worthy and reflect their personal and different opinions and points of view; none of these trust statements is wrong by definition.
Since trust statements are subjective, they are not necessarily symmetric. For example, in the figure above, Alice expresses trust in Carol as 0.1 while Carol expresses trust in Alice (reciprocates) as 0.3.
Hence a trust network is a directed, possibly weighted, asymmetric graph.