  We propose a holographic entanglement negativity conjecture involving the
bulk geometry, for mixed states of adjacent intervals in $(1+1)$-dimensional
dual conformal field theories through the $AdS/CFT$ correspondence. The
holographic entanglement negativity is obtained from a specific algebraic sum
of the geodesics anchored on respective intervals on the boundary which reduces
to the holographic mutual information between them. Utilizing our conjecture we
obtain the entanglement negativity of adjacent intervals in zero and finite
temperature ($1+1$)-dimensional holographic conformal field theories dual to
the bulk $AdS_3$ vacuum and the Euclidean BTZ black hole respectively. Our
holographic conjecture exactly reproduces the conformal field theory results
obtained through the replica technique, in the large central charge limit. We
briefly elucidate the corresponding issue for the $AdS_{d+1}/CFT_d$ scenario.
