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→Maximum Matching
By calculating the maximum matchings of a wide range of real networks, Liu et al. asserted that the number of driver nodes is determined mainly by the networks degree distribution <math>P(k_\mathrm{in}, k_\mathrm{out})</math>. They also calculated the average number of driver nodes for a network ensemble with arbitrary degree distribution using the cavity method. It is interesting that for a chain graph and a weak densely connected graph, both of which have very different in and out degree distributions; the formulation of Liu et al. would predict same values of <math>{n_\mathrm{D}}</math>. Also, for many real-word networks, namely, food webs, neuronal and metabolic networks, the mismatch in values of <math>{n_\mathrm{D}}^{real}</math> and <math>{n_\mathrm{D}}^\mathrm{rand\_degree}</math> calculated by Liu et al. is notable. If controllability is decided purely by degree, why are <math>{n_\mathrm{D}}^{real}</math> and <math>{n_\mathrm{D}}^\mathrm{rand\_degree}</math> so different for many real world networks? It remains open to scrutiny whether control robustness" in networks is influenced more by using betweenness centrality and closeness centrality over degree (graph theory) based metrics.
By calculating the maximum matchings of a wide range of real networks, Liu et al. asserted that the number of driver nodes is determined mainly by the networks degree distribution <math>P(k_\mathrm{in}, k_\mathrm{out})</math>. They also calculated the average number of driver nodes for a network ensemble with arbitrary degree distribution using the cavity method. It is interesting that for a chain graph and a weak densely connected graph, both of which have very different in and out degree distributions; the formulation of Liu et al. would predict same values of <math>{n_\mathrm{D}}</math>. Also, for many real-word networks, namely, food webs, neuronal and metabolic networks, the mismatch in values of <math>{n_\mathrm{D}}^{real}</math> and <math>{n_\mathrm{D}}^\mathrm{rand\_degree}</math> calculated by Liu et al. is notable. If controllability is decided purely by degree, why are <math>{n_\mathrm{D}}^{real}</math> and <math>{n_\mathrm{D}}^\mathrm{rand\_degree}</math> so different for many real world networks? It remains open to scrutiny whether control robustness" in networks is influenced more by using betweenness centrality and closeness centrality over degree (graph theory) based metrics.
通过计算各种真实网络的最大匹配，Liu等人断言驱动程序节点的数量主要由网络度分布<math>P(k_\mathrm{in}，k_\mathrm{out})</math>决定。他们还使用空腔方法计算了具有任意程度分布的网络集合的驱动节点的平均数量。有趣的是，对于'''<font color="#FF8000">链图 Chain Graph </font>'''和'''<font color="#FF80000">弱密集连通图 Weak Densely Connected Graph </font>'''，两者都具有非常不同的进出度分布；Liu等人的公式将预测<math>{n_\mathrm{D}}</math>的相同值。此外，对于许多真实词网络，即食物网、神经元和代谢网络，Liu等人计算的<math>{n/mathrm{D}^{real}</math>和<math>{n/mathrm{D}^\mathrm{rand\_degree}</math>值的不匹配。值得注意的是。如果可控性纯粹由度决定，那为什么<math>{n_\mathrm{D}}^{real}</math>和<math>{n_\mathrm{D}}^\mathrm{rand\_degree}</math>对于许多现实世界的网络来说是如此不同？对于网络中的控制鲁棒性是否更多地受到使用基于度（图论）的度量的'''<font color="#FF8000">中介中心性 Betweenness Centrality </font>'''和'''<font color="#FF8000">紧密度中心性 Closeness Centrality </font>'''的影响，仍然是开放的。