With emergence of blockchain technologies and the associated cryptocurrencies, such as Bitcoin, understanding network dynamics behind Blockchain graphs has become a rapidly evolving research direction. Unlike other financial networks, such as stock and currency trading, blockchain based cryptocurrencies have the entire transaction graph accessible to the public (i.e., all transactions can be downloaded and analyzed). A natural question is then to ask whether dynamics of the transaction graph impacts price of the underlying cryptocurrency. We show that standard graph features such as degree distribution of the transaction graph may not be sufficient to capture network dynamics and its potential impact on fluctuations of Bitcoin price. In contrast, topological features computed from the blockchain graph using the tools of persistent homology, are found to exhibit higher utility for predicting Bitcoin price dynamics.