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→Strong Triadic Closure Property and local bridges
==Strong Triadic Closure Property and local bridges==
==Strong Triadic Closure Property and local bridges==
'''<font color="#FF8000">强三元闭包性 Strong Triadic Closure Property </font>'''和'''<font color="#FF8000">本地网桥 Local Bridges </font>'''<br>
Strong Triadic Closure Property is that if a node has strong ties to two neighbors, then these neighbors must have at least a weak tie between them. A [[local bridge]] occurs, on the other hand, when a node is acting as a gatekeeper between two neighboring nodes who are not otherwise connected. In a network that follows the Strong Triadic Closure Property, one of the ties between nodes involved in a local bridge needs to be a weak tie.
Strong Triadic Closure Property is that if a node has strong ties to two neighbors, then these neighbors must have at least a weak tie between them. A [[local bridge]] occurs, on the other hand, when a node is acting as a gatekeeper between two neighboring nodes who are not otherwise connected. In a network that follows the Strong Triadic Closure Property, one of the ties between nodes involved in a local bridge needs to be a weak tie.
Strong Triadic Closure Property is that if a node has strong ties to two neighbors, then these neighbors must have at least a weak tie between them. A local bridge occurs, on the other hand, when a node is acting as a gatekeeper between two neighboring nodes who are not otherwise connected. In a network that follows the Strong Triadic Closure Property, one of the ties between nodes involved in a local bridge needs to be a weak tie.
Strong Triadic Closure Property is that if a node has strong ties to two neighbors, then these neighbors must have at least a weak tie between them. A local bridge occurs, on the other hand, when a node is acting as a gatekeeper between two neighboring nodes who are not otherwise connected. In a network that follows the Strong Triadic Closure Property, one of the ties between nodes involved in a local bridge needs to be a weak tie.
强三元闭包性是，如果一个节点与两个邻居有牢固的联系，则这些邻居之间必须至少有一条弱联系。 另一方面，当节点充当两个其他未连接的相邻节点之间的网守时，则发生本地网桥。 在遵循“强三元闭合性”的网络中，本地网桥中涉及的节点之间的联系之一必须是弱联系。
==Proof by contradiction==
'''<font color="#FF8000">矛盾证明 Proof By Contradiction </font>'''<br>
Let node B be a local bridge between nodes A and C such that there is no weak tie between the nodes involved. Therefore, B has a strong tie to both A and C. By the definition of Strong Triadic Closure, a weak tie would develop between nodes A and C. However, this contradicts the fact that B is a local gatekeeper. Thus at least one of the nodes involved in a local bridge needs to be a weak tie to prevent triadic closure from occurring.
Let node B be a local bridge between nodes A and C such that there is no weak tie between the nodes involved. Therefore, B has a strong tie to both A and C. By the definition of Strong Triadic Closure, a weak tie would develop between nodes A and C. However, this contradicts the fact that B is a local gatekeeper. Thus at least one of the nodes involved in a local bridge needs to be a weak tie to prevent triadic closure from occurring.
假设节点B是节点A和C之间的本地桥梁，以使所涉及的节点之间没有弱联系。 因此，B与A和C都具有牢固的联系。根据“强三元闭包性”的定义，节点A和C之间将形成弱联系。但是，这与B是本地网守的事实相矛盾。 因此，本地网桥中涉及的至少一个节点需要是弱连接，以防止三元闭包的发生。
==References==
==References==