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第114行：
第114行： − + 第120行：
第120行： − 随机故障的节点或定向攻击网络关键组成部分的枢纽。在网络枢纽节点的随机失效过程中，网络的鲁棒性是由节点的随机失效决定的。< ref > { cite journal | title = Resilience of the Internet to Random breaks | + − journal=Phys. Rev. Lett.|+ − − journal=Phys. Rev. Lett.| − − 日记 = 体育。牧师。李特 | − − year=2000| − − year=2000| − − 2000年 − − first=Reoven| − − first=Reoven| − − 1 = Reoven | − − last=Cohen| − − last=Cohen| − − 最后 = Cohen | − − first2=K. |last2=Erez |first3=D. |last3=ben-Avraham |first4=S.|last4=Havlin|authorlink4=Shlomo Havlin| − − first2=K. |last2=Erez |first3=D. |last3=ben-Avraham |first4=S.|last4=Havlin|authorlink4=Shlomo Havlin| − − 首先2 = k。2 = Erez | first3 = d.3 = ben-Avraham | first4 = s | last4 = Havlin | authorlink4 = Shlomo Havlin | − − volume=85| − − volume=85| − − 85 | − − pages=4626–8| − − pages=4626–8| − − 页数 = 4626-8 − − doi= 10.1103/PhysRevLett.85.4626| − − doi= 10.1103/PhysRevLett.85.4626| − − Doi = 10.1103/physrvlett. 85.4626 | − − url=http://link.aps.org/doi/10.1103/PhysRevLett.85.4626 − − url=http://link.aps.org/doi/10.1103/PhysRevLett.85.4626 − − Http://link.aps.org/doi/10.1103/physrevlett.85.4626 − − |bibcode=2000PhRvL..85.4626C|arxiv = cond-mat/0007048 |pmid=11082612}} − − |bibcode=2000PhRvL..85.4626C|arxiv = cond-mat/0007048 |pmid=11082612}} − − | bibcode = 2000PhRvL. . 85.4626 c | arxiv = cond-mat/0007048 | pmid = 11082612} − − </ref> The chance that a random failure would delete the hub is very small, because hubs coexists with a large number of small degree nodes. The removal of small degree nodes does not have a large effect on integrity of network. Even though the random removal would hit the hub, the chance of fragmantation of network is very small because the remaining hubs would hold the network together. In this case, hubs are the strength of a scale-free networks. − − </ref> The chance that a random failure would delete the hub is very small, because hubs coexists with a large number of small degree nodes. The removal of small degree nodes does not have a large effect on integrity of network. Even though the random removal would hit the hub, the chance of fragmantation of network is very small because the remaining hubs would hold the network together. In this case, hubs are the strength of a scale-free networks. − − 由于枢纽与大量小度节点共存，随机故障删除它的几率很小。而去除小节点对网络的完整性影响不大。即使随机删除会作用到上枢纽，'''<font color="#ff8000">网络碎片化 Fragmantation of Network</font>'''的可能性也非常小，因为剩余的枢纽仍能将网络连接在一起。在这种情况下，枢纽就是无标度网络的中坚力量。 + + 第194行：
第132行： − 在对枢纽进行有针对性的攻击时，网络的完整性会相对较快地崩溃。由于小节点主要连接到枢纽节点，对最大枢纽的攻击会在短时间内破坏网络。2008年的金融市场崩溃就是这种网络失灵的一个例子，当时最大的参与者(枢纽)的破产导致了整个系统的持续崩溃。另一方面，去除恐怖主义网络中的枢纽节点可能会产生积极的影响，目标节点的消失可能会摧毁整个恐怖组织。网络的攻击容忍度可以通过连接其外围节点来提高，但是它需要加倍的链接数量。+ −
→鲁棒性和攻击容忍度 Robustness and Attack Tolerance
当旧的枢纽被隐藏在网络中时，这种现象便在真实网络中出现。这种现象导致了网络演化和拓扑结构的变化。<ref>[http://barabasi.com/networksciencebook/content/book_chapter_6.pdf Barabási, Albert-László. ''Network Science: Evolving Networks''., p. 3]</ref> 老化现象的例子可参照 Facebook 超越了网络中最大的枢纽 Google (自2000年以来最大的节点)。
当旧的枢纽被隐藏在网络中时，这种现象便在真实网络中出现。这种现象导致了网络演化和拓扑结构的变化。<ref>[http://barabasi.com/networksciencebook/content/book_chapter_6.pdf Barabási, Albert-László. ''Network Science: Evolving Networks''., p. 3]</ref> 老化现象的例子可参照 Facebook 超越了网络中最大的枢纽 Google (自2000年以来最大的节点)。
=== '''<font color="#ff8000">鲁棒性和攻击容忍度 Robustness and Attack Tolerance</font>''' ===
===Robustness and Attack Tolerance 鲁棒性和抗毁性===
During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|
During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|
During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|
During the random failure of nodes or targeted attack hubs are key components of the network. During the random failure of nodes in network hubs are responsible for exceptional robustness of network.<ref>{{cite journal|title=Resilience of the Internet to Random Breakdowns|
当节点发生随机故障或特定攻击时，枢纽是网络的重要构件。当网络中的节点发生随机故障时，枢纽影响网络的鲁棒性。
The chance that a random failure would delete the hub is very small, because hubs coexists with a large number of small degree nodes. The removal of small degree nodes does not have a large effect on integrity of network. Even though the random removal would hit the hub, the chance of fragmantation of network is very small because the remaining hubs would hold the network together. In this case, hubs are the strength of a scale-free networks.
The chance that a random failure would delete the hub is very small, because hubs coexists with a large number of small degree nodes. The removal of small degree nodes does not have a large effect on integrity of network. Even though the random removal would hit the hub, the chance of fragmantation of network is very small because the remaining hubs would hold the network together. In this case, hubs are the strength of a scale-free networks.
由于枢纽与大量小度节点共存，随机故障删除枢纽的几率很小。而去除小度节点对网络的完整性影响不大。即使随机删除会作用到上枢纽，'''<font color="#ff8000">网络碎片化 Fragmantation of Network</font>'''的可能性也非常小，因为剩余的枢纽仍能将网络连接在一起。在这种情况下，枢纽就是无标度网络的中坚力量。
During a targeted attack on hubs, the integrity of a network will fall apart relatively fast. Since small nodes are predominantly linked to hubs, the targeted attack on the largest hubs results in destroys the network in a short period of time. The financial market meltdown in 2008 is an example of such a network failure, when bankruptcy of the largest players (hubs) led to a continuous breakdown of the whole system.<ref>{{Cite journal|author1=S. V. Buldyrev |author2=R. Parshani |author3=G. Paul |author4=H. E. Stanley |author5=S. Havlin |title = Catastrophic cascade of failures in interdependent networks|journal = Nature |volume = 464 |pages = 1025–28 |year = 2010 | doi=10.1038/nature08932 |issue=7291|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all |pmid=20393559|arxiv=1012.0206 |bibcode=2010Natur.464.1025B }}</ref> On the other hand, it may have a positive effect when removing hubs in a terrorist network; targeted node deletion may destroy the whole terrorist group. The attack tolerance of a network may be increased by connecting its peripheral nodes, however it requires to double the number of links.
During a targeted attack on hubs, the integrity of a network will fall apart relatively fast. Since small nodes are predominantly linked to hubs, the targeted attack on the largest hubs results in destroys the network in a short period of time. The financial market meltdown in 2008 is an example of such a network failure, when bankruptcy of the largest players (hubs) led to a continuous breakdown of the whole system.<ref>{{Cite journal|author1=S. V. Buldyrev |author2=R. Parshani |author3=G. Paul |author4=H. E. Stanley |author5=S. Havlin |title = Catastrophic cascade of failures in interdependent networks|journal = Nature |volume = 464 |pages = 1025–28 |year = 2010 | doi=10.1038/nature08932 |issue=7291|url=http://havlin.biu.ac.il/Publications.php?keyword=Catastrophic+cascade+of+failures+in+interdependent+networks&year=*&match=all |pmid=20393559|arxiv=1012.0206 |bibcode=2010Natur.464.1025B }}</ref> On the other hand, it may have a positive effect when removing hubs in a terrorist network; targeted node deletion may destroy the whole terrorist group. The attack tolerance of a network may be increased by connecting its peripheral nodes, however it requires to double the number of links.
During a targeted attack on hubs, the integrity of a network will fall apart relatively fast. Since small nodes are predominantly linked to hubs, the targeted attack on the largest hubs results in destroys the network in a short period of time. The financial market meltdown in 2008 is an example of such a network failure, when bankruptcy of the largest players (hubs) led to a continuous breakdown of the whole system. On the other hand, it may have a positive effect when removing hubs in a terrorist network; targeted node deletion may destroy the whole terrorist group. The attack tolerance of a network may be increased by connecting its peripheral nodes, however it requires to double the number of links.
During a targeted attack on hubs, the integrity of a network will fall apart relatively fast. Since small nodes are predominantly linked to hubs, the targeted attack on the largest hubs results in destroys the network in a short period of time. The financial market meltdown in 2008 is an example of such a network failure, when bankruptcy of the largest players (hubs) led to a continuous breakdown of the whole system. On the other hand, it may have a positive effect when removing hubs in a terrorist network; targeted node deletion may destroy the whole terrorist group. The attack tolerance of a network may be increased by connecting its peripheral nodes, however it requires to double the number of links.
在对枢纽进行特定的攻击时，网络的完整性会相对较快地被破坏。由于小度节点大量的链接到枢纽，因此对最大枢纽的攻击会在短时间内破坏网络。2008年的金融市场崩溃就是这种网络失灵的一个例子，当时头号玩家（枢纽）的破产导致了整个系统的持续崩溃。另一方面，去除恐怖主义网络中的枢纽可能会产生积极的影响，特定节点的消失可能会摧毁整个恐怖组织。网络的抗毁性可以通过连接其外围节点来提高，但是它需要加倍的链接数量。
=== Degree correlation 度相关===
=== Degree correlation 度相关===