Why Laplacian matrix needs normalization and how come the sqrt-power of degree matrix? The symmetric normalized Laplacian matrix is [defined](http://en.wikipedia.org/wiki/Spectral_clustering) as
$$\ L = D^{1/2}AD^{-1/2}$$
where `L` is Laplacian matrix, `A` is adjacent matrix. Element $A\_{ij}$ represents a measure of the similarity between data points with indices $i$ and $j$. `D` is diagonal matrix, defined as $\ D = \sum\limits\_i A\_{ij}$. In other words, it is the sum of similarity from node $j$ to all its neighbor node $i$.

I can't figure out some question about the formula:

* **Why** we need to normalize `Laplacian Matrix` like that? $\ {1/2}$-power ?
* Is there any special reason?
* Is there any references?