Does a symmetric matrix with main diagonal zero is classified into a separate type of its own? And does it have a particular name? I have a symmetric matrix as shown below
$$\begin{pmatrix} 0&2&1&4&3 \\ 2&0&1&2&1 \\ 1&1&0&3&2 \\4&2&3&0&1 \\ 3&1&2&1&0\end{pmatrix}$$ 
Does this matrix belong to a particular type? 

I am CS student and not familiar with types of matrices. I am researching to know the particular matrix type since I have a huge collection of matrices similar to this one. By knowing the type of matrix, maybe I can go through its properties and work around easier ways to process data efficiently. I am working on a research project in Data Mining. Please help.
P.S.: Only the diagonal elements are zero. Non diagonal elements are positive.

This is a hollow matrix. You can say that the sum of its eigenvalues equals zero.
