Unweighted

Unweighted refers to a quantity, structure, or dataset that assigns equal importance or weight to all its components, with no numerical weights influencing calculations or decisions. In graph theory, an unweighted graph is a graph in which all edges have the same value, typically implicit as weight 1. Consequences include that path length corresponds to the number of edges in a path, rather than the sum of edge weights. Algorithms such as breadth-first search (BFS) efficiently compute shortest paths on unweighted graphs, and adjacency matrices store 1s for edges and 0s for absent edges. Degree of a vertex in an unweighted graph is the count of incident edges. Unweighted graphs are contrasted with weighted graphs, where edge weights reflect cost, distance, or capacity, and can affect pathfinding, clustering, and centrality measures.

In statistics and data analysis, an unweighted statistic treats all observations equally, such as the unweighted mean, which is the simple average of values. This is in contrast to a weighted mean where observations contribute proportionally to assigned weights, often reflecting sample design, frequency, or importance. In survey sampling, unweighted data may be used for exploratory analysis, while weighted data adjusts for unequal selection probabilities or nonresponse.

Unweighted concepts appear in other domains as well, including network science, coding, and decision-making, where simplicity or equal treatment is preferred or required. When weights exist, they must be explicitly defined; when they do not, analyses use counts, incidences, or equal contributions.