The ABC (atom-bond connectivity) matrix 
of a simple graph is a weighted
adjacency matrix with weight
 |
(1)
|
where 
are the vertex
degrees of the graph. In other words,
![[A_(ABC)]_(ij)={sqrt((d_i+d_j-2)/(d_id_j)) for i,j adjacent; 0 otherwise](/images/equations/ABCMatrix/NumberedEquation2.svg) |
(2)
|
(Zheng et al. 2022).
It was introduced by Estrada et al. (2017) to model the enthalpy of formation of alkanes (Zheng et al. 2023).
Its largest eigenvalue 
is called the ABC
spectral radius, half the sum of its matrix elements is the ABC
index, and the sum of absolute values of its eigenvalues
is the ABC energy.
