灾难、海滩球和雏菊的等时类
Isotemporal classes of diasters, beachballs, and daisies
摘要：
如果组成网络的顶点在不同的时间点交互，这些交互的时间顺序和网络的图结构足以传达信息在网络中流动的路线。两个具有实值边标签的网络是时间同构的，如果存在一个图同构f：N->M，它保持时间路径-其中序列边标签严格增加的路径。时间同构网络的等价类称为等时类。确定特定图结构N（G）的等时类的数目的方法是不明显的，并且难以用传统的技术，如Pólya枚举（Pólya，1937）。在这里，我提出了一个简单的公式的数量isotemporal类的diasters，图组成的一个顶点的度a+1连接到一个顶点的度b+1，与所有其他顶点的度1（表示D（a，b））。特别地，如果a不等于b，则N（D（a，b）=ab+a+b+1，否则N（D（a，a）=（1/2）（a^2+3a+2）。这个公式然后被扩展到五个其他类型的伪图的应用定理，状态N（G）是保持两个图类型之间，如果边缘邻接和自同构，并提供任何两个网络是同一个isotemporal类的成员，当且仅当它们是同构的顺序边标签的非邻边的换位。
英文摘要：
If the vertices composing a network interact at distinct time points, the temporal ordering of these interactions and the network's graph structure are sufficient to convey the routes by which information can flow in the network. Two networks with real-valued edge labels are temporally isomorphic if there exists a graph isomorphism f:N->M that preserves temporal paths - paths in which sequential edge labels are strictly increasing. An equivalence class of temporally ismorphic networks is known as an isotemporal class. Methods to determine the number of isotemporal classes of a particular graph structure N(G) are non-obvious, and refractory to traditional techniques such as Pólya enumeration (Pólya, 1937). Here, I present a simple formula for the number of isotemporal classes of diasters, graphs composed of a vertex of degree a+1 connected to a vertex of degree b+1, with all other vertices of degree 1 (denoted D(a,b)). In particular, N(D(a,b)))=ab+a+b+1 if a is not equal to b, and N(D(a,a)))=(1/2) (a^2+3a+2) otherwise. This formula is then extended to five additional types of pseudograph by application of a theorem that states N(G) is preserved between two graph types if edge adjacencies and automorphisms are preserved, and provided that any two networks are members of the same isotemporal class if and only if they are isomorphic by transpositions of sequential edge labels on non-adjacent edges.
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