论文标题
使用Foundor同源性的加权Quiver内核
A Weighted Quiver Kernel using Functor Homology
论文作者
论文摘要
在本文中，我们提出了一种研究加权定向网络的新型同源方法。我们的此类网络模型是一个有向图$ Q $，配备了$ q $中的箭头的$ q_ {1} $上的重量函数$ w $。我们要求我们的重量功能的范围$ w $配备了加法或乘法，即$ w $是数学术语中的单体。当$ w $配备在矢量空间$ m $上的表示时，同源代数的标准方法使我们能够定义同源组$ h _ {*}（q，w; m）$。众所周知，当$ q $没有方向的周期时，$ h_ {n}（q，w; m）= 0 $ for $ n \ ge 2 $和$ h_ {1}（q，q，w; m）$可以轻松计算。这一事实使我们能够为加权有向图定义新的图表。我们用真实数据进行了两个示例计算，发现我们的方法实际上适用。
In this paper, we propose a new homological method to study weighted directed networks. Our model of such networks is a directed graph $Q$ equipped with a weight function $w$ on the set $Q_{1}$ of arrows in $Q$. We require that the range $W$ of our weight function is equipped with an addition or a multiplication, i.e., $W$ is a monoid in the mathematical terminology. When $W$ is equipped with a representation on a vector space $M$, the standard method of homological algebra allows us to define the homology groups $H_{*}(Q,w;M)$. It is known that when $Q$ has no oriented cycles, $H_{n}(Q,w;M)=0$ for $n\ge 2$ and $H_{1}(Q,w;M)$ can be easily computed. This fact allows us to define a new graph kernel for weighted directed graphs. We made two sample computations with real data and found that our method is practically applicable.
