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第73行：
第73行： − + 第79行：
第79行： − 术语“圈”也可以指图的圈空间的一个元素。有许多圈空间，每个系数域或环都有一个圈空间。最常见的是二元循环空间(通常简称为循环空间) ，它由在每个顶点具有偶度的边集组成，它在二元域上形成一个向量空间。根据维布伦定理，圈空间中的每个元素都可以构成简单圈的边不交并。图的圈基是构成圈空间基的一组简单圈。+ 第87行：
第87行： − 利用代数拓扑的思想，二元循环空间可以推广到其他环上的向量空间或模，如整数、有理数或实数等。+ − −
→Cycle space
一个图中的边环具有以下性质：不在此边环上的两条连边可以通过一条特殊路径连接，该路径内部顶点均不在此边环上。如果一个图中的某条环并非通过加一条边形成，那么其边环肯定是诱导环。
一个图中的边环具有以下性质：不在此边环上的两条连边可以通过一条特殊路径连接，该路径内部顶点均不在此边环上。如果一个图中的某条环并非通过加一条边形成，那么其边环肯定是诱导环。
== Cycle space ==
== Cycle space 环空间 ==
The term ''cycle'' may also refer to an element of the [[cycle space]] of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the ''binary cycle space'' (usually called simply the ''cycle space''), which consists of the edge sets that have even degree at every vertex; it forms a [[vector space]] over the two-element [[finite field|field]]. By [[Veblen's theorem]], every element of the cycle space may be formed as an edge-disjoint union of simple cycles. A [[cycle basis]] of the graph is a set of simple cycles that forms a [[basis (linear algebra)|basis]] of the cycle space.<ref name="gy">{{citation|title=Graph Theory and Its Applications|edition=2nd|first1=Jonathan L.|last1=Gross|first2=Jay|last2=Yellen|publisher=CRC Press|year=2005|isbn=9781584885054|chapter=4.6 Graphs and Vector Spaces|pages=197–207|url=https://books.google.com/books?id=-7Q_POGh-2cC&pg=PA197}}.</ref>
The term ''cycle'' may also refer to an element of the [[cycle space]] of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the ''binary cycle space'' (usually called simply the ''cycle space''), which consists of the edge sets that have even degree at every vertex; it forms a [[vector space]] over the two-element [[finite field|field]]. By [[Veblen's theorem]], every element of the cycle space may be formed as an edge-disjoint union of simple cycles. A [[cycle basis]] of the graph is a set of simple cycles that forms a [[basis (linear algebra)|basis]] of the cycle space.<ref name="gy">{{citation|title=Graph Theory and Its Applications|edition=2nd|first1=Jonathan L.|last1=Gross|first2=Jay|last2=Yellen|publisher=CRC Press|year=2005|isbn=9781584885054|chapter=4.6 Graphs and Vector Spaces|pages=197–207|url=https://books.google.com/books?id=-7Q_POGh-2cC&pg=PA197}}.</ref>
The term cycle may also refer to an element of the cycle space of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the binary cycle space (usually called simply the cycle space), which consists of the edge sets that have even degree at every vertex; it forms a vector space over the two-element field. By Veblen's theorem, every element of the cycle space may be formed as an edge-disjoint union of simple cycles. A cycle basis of the graph is a set of simple cycles that forms a basis of the cycle space.
The term cycle may also refer to an element of the cycle space of a graph. There are many cycle spaces, one for each coefficient field or ring. The most common is the binary cycle space (usually called simply the cycle space), which consists of the edge sets that have even degree at every vertex; it forms a vector space over the two-element field. By Veblen's theorem, every element of the cycle space may be formed as an edge-disjoint union of simple cycles. A cycle basis of the graph is a set of simple cycles that forms a basis of the cycle space.
关于术语“环Cycle”还可以指代一个图中环空间的一个元素。在一个图中，存在很多环空间，每个都有对应的系数域Coefficient field或环Ring（代数）。最常见的是二元环空间（通常简称为环空间），它是由在该图中每个顶点上具有偶数度的边集组成。它在二元域上形成了一个向量空间。根据维布伦定理Veblen's theorem，该环空间的每个元素都可以形成为简单环的不相交边的并集。该图的环基相当于一组简单环，它们构成了环空间的基。
Using ideas from algebraic topology, the binary cycle space generalizes to vector spaces or modules over other rings such as the integers, rational or real numbers, etc.
Using ideas from algebraic topology, the binary cycle space generalizes to vector spaces or modules over other rings such as the integers, rational or real numbers, etc.
根据代数拓扑Algebraic topology的思想，二元环空间Binary cycle space可以推广为其他环Ring中的向量空间Vector spaces或模Module，例如整数，有理数或实数等。。
== Cycle detection ==
== Cycle detection ==