# Application of Graph Theory for Blockchain Technologies
###### Abstract  
Blockchain technology, serving as the backbone for decentralized systems, facilitates secure and transparent transactional data storage across a distributed network of nodes. Blockchain platforms rely on distributed ledgers to enable secure peer-to-peer transactions without central oversight. As these systems grow in complexity, analyzing their topological structure and vulnerabilities requires robust mathematical frameworks. This paper explores applications of graph theory for modeling blockchain networks to evaluate decentralization, security, privacy, scalability and NFT Mapping. We use graph metrics like degree distribution and betweenness centrality to quantify node connectivity, identify network bottlenecks, trace asset flows and detect communities. Attack vectors are assessed by simulating adversarial scenarios within graph models of blockchain systems. Overall, translating blockchain ecosystems into graph representations allows comprehensive analytical insights to guide the development of efficient, resilient decentralized infrastructures. graph theory; blockchain; graph model 20242020242  
insights to guide the development of efficient, resilient decentralized digital ledgers and techniques to analyze blockchain systems and address challenges in their design and operation. An extensive application of network science is beyond the scope of this work. Table 1 presents a holistic summary of graph theory's contribution and proofs that can provide insight and improvement to blockchain technology. Graph theory has been widely recognized for its diverse applications across various fields. [PERSON] et al. [5] discuss the applications of graph coloring in different practical scenarios, highlighting the versatility of graph theory. Similarly, [PERSON] and [PERSON] [6] emphasize the extensive use of graphs in computer science and social networks, showcasing the relevance of graph theory in modern technological domains. [PERSON] et al. [7] delve into the significance of domination in graph theory and its wide applicability in different fields. Moreover, [PERSON] et al. [8] showcase the interdisciplinary nature of algebraic graph theory, indicating its potential for future applications. [PERSON] et al. [9] explore the application of graph theory in plasma chemical reaction engineering, demonstrating how graph visualization and algorithms can aid in analyzing reaction networks. [PERSON] and [PERSON] [10] discuss the applications of mutually orthogonal graph squares in various communication and design domains, showcasing the practical implications of graph theory concepts. Graph theory was also explored to solve many real-world problems with multi-dynamic and rapidly evolving characteristics. It provides an apt abstraction for modeling the topological structure and interactions within blockchain networks. Some of the recent applications demonstrated by researchers include advanced treatment for epilepsy based on Epileptogenic Zone localization [11], network vulnerability analysis by finding the secure dominating set [12], Alzheimer's Disease investigation [13], and techniques to place PMU in an electrical power network [14]. But the list is not comprehensive, Table 2's references collectively highlight the broad spectrum of applications of graph theory in a wide range of the computer science field. Graph theory has been applied in various ways in the field of blockchain. [PERSON] et al. [35] use hypergraphs to create a blockchain model that reduces storage consumption and enhances security. [PERSON] et al. [36] incorporate graph models in blockchain functionality, allowing for data analysis and visualization of changes in blockchain data. [PERSON] et al. [37] find that topological features computed from the blockchain graph using persistent homology are useful in predicting Bitcoin price dynamics. [PERSON] et al. [38] use graph neural networks for DApp fingerprinting, where a graph structure called Traffic Interaction Graph (TIG) is used to represent