Representing modern data using graphs has become more prominent in recent years. The gradual increasing size and complex structure of graphs made many classical algorithms slow. Meanwhile, graphs like social and web networks evolve over time. Traditional graph analysis that expects a fixed data set is not sufficient for these kinds of temporal graphs. It is necessary to take advantage of the modern HPC architecture and customize the applications to enhance the performance and to keep the runtime of the analysis low.First, this dissertation analyzes modern vector architectures for graph analysis kernels. We evaluate the performance achieved on two different architectures (Skylake and Cascade Lake) and show that good hardware support for scatter instructions is necessary to fully leverage vector processing for graph partitioning problems. Then we build a performance model that analyzes the performance of graph applications for given computer architecture. We study sparse matrix-vector multiplication (SpMV) as a representative application for performance models on distributed systems, since many applications rely on basic sparse linear algebra operations from numerical solvers to graph analysis algorithms. We proposed the first model of runtime for SpMV on distributed memory machines that accounts for platform and graph structure.Then we consider dynamically evolving graphs. In this work, we show the performance analysis of Pagerank on the temporal graphs. Many algorithms have been proposed to compute Pagerank on evolving graphs; most of them focus on incremental ways to study temporal graphs. But the question is ``if the complete data is available at the beginning of the process, and we want to know the properties of the graph over time, should we still use the streaming graph algorithm for temporal graph analysis?" We call this type of temporal analyses Postmortem graph analysis. In \textit{Postmortem} analysis, one performs graph analysis on multiple subgraphs based on a well-defined time-interval. In contrast, streaming algorithms mainly focus on gradually updating properties based on events like edge addition or deletion graph analysis. We show that \textit{Postmortem} graph analysis can provide better Pagerank performance on temporal graphs than a streaming analysis.