The arithmetic of N, Z, Q, R can be extended to a graph arithmetic where N is the semiring of finite simple graphs and where Z and Q are integral domains, culminating in a Banach algebra R. A single network completes to the Wiener algebra. We illustrate the compatibility with topology and spectral theory. Multiplicative linear functionals like Euler characteristic, the Poincare polynomial or the zeta functions can be extended naturally. These functionals can also help with number theoretical questions. The story of primes is a bit different as the integers are not a unique factorization domain, because there are many additive primes. Most graphs are multiplicative primes.

翻译：N、Z、Q、R的算术可以扩展为图形算术,其中N是限定的简单图形的半环,Z和Q是整体域,最终形成Banach代数R。一个单一的网络完成到Wiener代数。我们演示了与地形学和光谱理论的兼容性。倍增线性功能,如Euler 特性、Poincare 多元性或zeta函数,可以自然扩展。这些函数也可以帮助解决数字理论问题。质数的故事有些不同,因为整数不是一个独特的因子化域,因为有多种添加质。大多数图形是多倍化质。