论文标题
加权图上的ollivier ricci-flow
Ollivier Ricci-flow on weighted graphs
论文作者
论文摘要
我们研究了在加权图上定义的ollivier-lin-lu-yau曲率的RICCI流动方程的溶液的存在。我们的工作是由\ cite {nllg}激励的，在\ cite {nllg}中，RICCI流量算法已成功地应用于检测复杂网络的一种离散几何方法。我们的主要结果是解决连续时间归一化RICCI流动的解决方案的存在和唯一定理。我们还向路径图上的RICCI流程显示了可能的解决方案，并证明了有限星图上的RICCI流，至少三片叶子会收敛到恒定恒星。
We study the existence of solutions of Ricci flow equations of Ollivier-Lin-Lu-Yau curvature defined on weighted graphs. Our work is motivated by\cite{NLLG} in which the discrete time Ricci flow algorithm has been applied successfully as a discrete geometric approach in detecting complex networks. Our main result is the existence and uniqueness theorem for solutions to a continuous time normalized Ricci flow. We also display possible solutions to the Ricci flow on path graph and prove the Ricci flow on finite star graph with at least three leaves converges to constant-weighted star.
