Create a program to collect at least 500 Wikipedia pages and links from these pages to other Wikipedia pages. Collect similarity data for each page using word frequencies and/or word2vec. Report the number of spanning trees (for any arbitrary node as initial starting point) as a connectivity check. Utilize caching to avoid unnecessary reconstruction. Then write a UI to read the graph, allowing the using to select any two pages (by title) and display graphically the shortest (weighted by any similarity metric) path between them, if one exists, as well as the most similar node for each.