Efficient node representation for weighted networks is an important problem for many domains in real-world network analysis. Network exploration usually comes down to description of some structural features which give information about network properties in general, but not about specific nodes. Whereas information about node profile is very important in any network with attributed nodes. Recently, the network embedding approach has emerged, which could be formalized as mapping each node in the undirected and weighted graph into a d-dimensional vector that captures its structural properties. The output representation can be used as the input for a variety of data analysis tasks as well as for individual node analysis. We suggested using an additional approach for node description based on the topological structure of the network. Some interesting topological features of such data can be revealed with topological data analysis. Each node in this case may be described in terms of participation in topological cavities of different sizes and their persistence. Such representation was used as an alternative node description and demonstrated their efficiency in the community detection task. In order to test the approach, we used a weighted stochastic block model with different parameters as a network generative process.