In mathematics, the energy of a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

is the sum of the absolute values of the

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...

s of the

adjacency matrix In graph theory and computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. In the special case of a finite simp ...

of the graph. This quantity is studied in the context of spectral graph theory. More precisely, let ''G'' be a graph with ''n'' vertices. It is assumed that ''G'' is

simple Simple or SIMPLE may refer to: *Simplicity, the state or quality of being simple Arts and entertainment * ''Simple'' (album), by Andy Yorke, 2008, and its title track * "Simple" (Florida Georgia Line song), 2018 * "Simple", a song by Johnn ...

, that is, it does not contain loops or parallel edges. Let ''A'' be the

of ''G'' and let

\lambda_i

i = 1 , \ldots , n

, be the eigenvalues of ''A''. Then the energy of the graph is defined as: :

E(G) = \sum_^n, \lambda_i, .

References

*. *. *. *. Algebraic graph theory {{graph-stub