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).
