Number of connected components

Every matroid decomposes uniquely as a direct sum $M = M|E_1 \oplus \dots \oplus M|E_k$ of connected matroids. The sets $E_i$ are the connected components: two distinct elements are in the same component exactly when some circuit contains both. This column is $k$. Copied from polyDB (N_CONNECTED_COMPONENTS).

This is a property of the matroid. Do not confuse it with n_components, which counts components of the realization space.