The computational complexities posed by large-scale graph theory issues are hinged on the substantial size and intricacy of the data. Analyzing graphs measuring millions or billions of edges and nodes necessitates immense memory and processing capabilities, requirements frequently beyond the purview of traditional algorithms and hardware. The intricacy of numerous graph algorithms surges in tandem with the graph's size, compounding activities like community detection, shortest path computation, and graph partitioning in terms of computational demands. Additionally, real-world graphs' irregular, rare structure complicates efficient data storage and parallelization. Scalability problems arise as algorithms should juggle resource consumption, speed, and accuracy while capably responding to dynamic graph structure changes. Surmounting these challenges entails creative algorithmic constructs, data compression methods, and distributed computing frameworks to facilitate comprehensive analyses of large-scale graphs in practical durations.