The first Zagreb index for a graph with vertex count and vertex degrees for , ..., is defined by
The notations (e.g., Lin et al. 2023) and (e.g., Devillers and Balaban 2000) are variously used.
The first Zagreb matrix is related to earlier indices (defined by Platt) and (defined by Gordon and Scantlebury) by
where is the edge count of a graph (Devillers and Balaban p. 27, 2000).