1. A computer-implemented method executed by one or more processors, the method comprising: maintaining data in a distributed computing system, the data describing a graph representing relationships among items, the graph having a plurality of vertices representing the items, and having a plurality of edges connecting the plurality of vertices representing the relationships among the items; identifying a new label value for a first vertex, the first vertex connected to a second vertex by an edge, the first vertex including a first label value indicating a strength of association between the first vertex and a particular label, the second vertex including a second label value indicating a strength of association between the second vertex and the particular label, and the edge including an edge label value indicating a degree to which the first label value affects the second label value, wherein the particular label, for which the first label value and the second label value respectively indicate a strength of association with the first vertex and the second vertex, represents a possible characteristic of the first vertex and the second vertex; in response to identifying the new label value: updating the first label value, indicating a strength of association between the first vertex and the particular label representing a possible characteristic of the first vertex and the second vertex, to the identified new label value; determining an updated label value for the second vertex based on the updated first label value for the first vertex and the edge label value, indicating a degree to which the first label value affects the second label value, for the edge connecting the first vertex to the second vertex; and updating the second label value, indicating a strength of association between the second vertex and the particular label representing a possible characteristic of the first vertex and the second vertex, to the updated label value; and outputting at least the second label value indicating a strength of association between the second vertex and the particular label.