  The paper is devoted to the study of finite dimensional complex evolution
algebras. The class of evolution algebras isomorphic to evolution algebras with
Jordan form matrices is described. For finite dimensional complex evolution
algebras the criteria of nilpotency is established in terms of the properties
of corresponding matrices. Moreover, it is proved that for nilpotent
$n-$dimensional complex evolution algebras the possible maximal nilpotency
index is $1+2^{n-1}.$ The criteria of planarity for finite graphs is formulated
by means of evolution algebras defined by graphs.
