  In this paper we study a construction of algebraic curves from combinatorial
data. In the study of algebraic curves through degeneration, graphs usually
appear as the dual intersection graph of the central fiber. Properties of such
graphs can be encoded in so-called tropical curves. Our main concern is the
relation between algebraic curves and tropical curves where the deformation
problem is obstructed. Particular emphasis is put on the role of higher valent
vertices of tropical curves, which has not been developed well so far in spite
of its importance in this area of study. We will give a general formula
describing the obstruction, a new criterion for the vanishing of the
obstruction, and a relation between the number of algebraic curves and the
number of integral points in certain polytopes. We also prove the optimal
version of the correspondence between tropical curves and algebraic curves when
the tropical curves are regular, generalizing previous results.
