The eigenvalues returned by EIG are not sorted in any particular order generally (for some special types of matrices (e.g. exactly symmetric), they might often be sorted in the same order, but we make no guarantees that this is always the case). For EIGS the eigenvalues are sorted in the order given by option sigma (e.g. 'largestabs', ...).
To sort the eigenvalues returned, just call sort after computing EIG:
or, for eigenvectors too,
[U, D] = eig(A);
[~, ind] = sort(diag(D));
D = D(ind, ind);
U = U(:, ind);
Since you are computing EIG of multiple matrices, if the lines describing each eigenvalue in your plot cross, this will not show continuous lines. It's not possible for each individual computation of eigenvalues to know about the connection to another, very similar, matrix A and its eigenvalues. In this case, the File Exchange package eigenshuffle that Ameer recommends may help you.