The cul-8752-parquet.tar.gz derivatives are in the Apache Parquet format, which is a columnar storage format. These derivatives are generally small enough to work with on your local machine, and can be easily converted to Pandas DataFrames. See this notebook for examples.
Gephi file, which can be loaded into Gephi. It will have basic characteristics already computed and a basic layout.
Raw Network file, which can also be loaded into Gephi. You will have to use that network program to lay it out yourself.
Full text file. In it, each website within the web archive collection will have its full text presented on one line, along with information around when it was crawled, the name of the domain, and the full URL of the content.
Domains count file. A text file containing the frequency count of domains captured within your web archive.