GLYPH<s48> GLYPH<s50> GLYPH<s48> GLYPH<s48> GLYPH<s52> GLYPH<s48> GLYPH<s48> GLYPH<s54> GLYPH<s48> GLYPH<s48> GLYPH<s49> GLYPH<s48> GLYPH<s45>GLYPH<s49> GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s49> GLYPH<s48> GLYPH<s51> GLYPH<s49> GLYPH<s48> GLYPH<s53> GLYPH<s49> GLYPH<s48> GLYPH<s55> GLYPH<s48> GLYPH<s50> GLYPH<s48> GLYPH<s48> GLYPH<s52> GLYPH<s48> GLYPH<s48> GLYPH<s54> GLYPH<s48> GLYPH<s48> GLYPH<s49> GLYPH<s48> GLYPH<s50> GLYPH<s49> GLYPH<s48> GLYPH<s51> GLYPH<s49> GLYPH<s48> GLYPH<s52> GLYPH<s82> GLYPH<s110> GLYPH<s32> GLYPH<s32> GLYPH<s82> GLYPH<s32>GLYPH<s82> GLYPH<s76> GLYPH<s44>GLYPH<s32>GLYPH<s76>GLYPH<s68>GLYPH<s80> GLYPH<s32>GLYPH<s82> GLYPH<s83> GLYPH<s44>GLYPH<s32>GLYPH<s83>GLYPH<s68>GLYPH<s80> GLYPH<s73>GLYPH<s110> GLYPH<s116>GLYPH<s101> GLYPH<s114>GLYPH<s110> GLYPH<s101> GLYPH<s116> GLYPH<s40>GLYPH<s98>GLYPH<s41> GLYPH<s32> GLYPH<s32> GLYPH<s32>GLYPH<s82> GLYPH<s76> GLYPH<s44>GLYPH<s32>GLYPH<s76>GLYPH<s68>GLYPH<s80> GLYPH<s32>GLYPH<s82> GLYPH<s83> GLYPH<s83>GLYPH<s68>GLYPH<s80> GLYPH<s40>GLYPH<s97>GLYPH<s41> GLYPH<s112> GLYPH<s111> GLYPH<s119> GLYPH<s101> GLYPH<s114>GLYPH<s32>GLYPH<s103> GLYPH<s114>GLYPH<s105> GLYPH<s100> and having an average degree 〈 k 〉 ≈ 3 . 88 . The variations of R as a function of n for both pinning strategies are plotted in Fig. 3(b). Again, we find a non-smooth decrease of R . For the Internet network, we find only one crossing between the two curves, which is located at about n = 2236 . The finding that heterogenous networks can be better con- trolled by pinning the small-degree nodes might have some potential applications, say, for example, in synchronizing sen- sor networks or controlling the consensus of multi-agent sys- tems. In a sensor network, due to terrain complexity the sen- sors are distributed in a non-uniform fashion: most of the sen- sors have very few neighbors, but a few sensors could have many neighbors [27]. That is, the sensor network has a het- erogenous degree distribution. To synchronize the timers of the sensors, a general approach is to assemble a fraction of the sensors with a signal receiver, which receives signal from the satellite and reset the timer of the sensors accordingly. For those sensors without the receiver, their timers are updated by their neighbors. Here an important question is that, for the given number of sensors having signal receiver, how to place them properly in order of a higher performance for timer syn- chronization? The study of the current paper suggests that, if the number of receiver-assembled sensors are large enough, it may be better to place them in the areas of sparse sensors. An- other application could be the control of consensus in multi- agent systems [28]. To make the mobile agents move in a synchronous fashion, in engineering one practical approach is to introduce some “leading” agents into the system. Differ- ent to the normal agents, these leading agents have a prede- fined motion, but they will influence the motion of the normal agents via couplings (behave like the pinning controller). Our study suggests that, to control the multi-agent system more ef- ficiently, we may choose to put the “leading” agents into the small swarms, instead of the tacitly believed large swarms. (From the network point of view, large and small swarms could be regarded as possessing large and small degree, re- spectively.) 4 FIG. 3: (Color online) Comparison of performance the two pinning strategies, LDP and SDP, for (a) the power-grid network of the west- ern United States and (b) the Internet at the Autonomous level. Eq. [7], which implies that Δ R = R $^{L}$− R S ∝ N . As the de- gree of heterogeneity of star networks can be characterized by the network size, this relation thus implies from another angle the superiority of SDP in controlling heterogeneous networks. It is worth noting that a similar phenomenon about the role of small-degree nodes has been also observed in network syn- chronization, where it is found that, to achieve global network synchronization, it is usually the smallest-degree nodes that are more important [24]. How about the realistic networks? The specific examples we have checked are the electrical power grid of the western United States [25] and the Internet at the autonomous level [26]. The power-grid network consists of N = 4941 nodes and has average degree 〈 k 〉 ≈ 2 . 67 . The variations of R as a function of n for both pinning strategies are plotted in Fig. 3(a). Interestingly, it is found that, different to the results of the ideal models [Fig. 1], the value of R is decreased in a non-smooth fashion and the two curves are crossed at several places. We attribute this phenomenon to the inherent commu- nity structures in the power-grid network (a detail analysis on the non-smooth variation of R will be presented elsewhere). The Internet we have employed consists of N = 6474 nodes In summary, we have compared the performance of two op- posite pinning strategies in controlling complex networks. It is found that, when a significant fraction of the network node s are pinned, the pinning of the small-degree nodes could have a higher performance than the large-degree ones. We have ex- plained this phenomenon by a model of simplified network, and discussed the dependence of this phenomenon to the net- work parameters in detail. These findings, hopefully, will p ro- vide a new angle to the pinning control of complex networks, and apply to practical situations. This work was supported by National Natural Science Foundation of China under Grant No. 10805038 and by Chi- nese Universities Scientific Fund. [1] G. Hu and Z. Qu, Phys. Rev. Lett. 72 , 68 (1994). [2] G. Hu, Z. Qu, and K.F. He, Int. J. Bifurcation and Chaos 5 , 901 [3] P.Y. Wang, P. Xie, J.H. Dai, and H.J. Zhang, Phys. Rev. Lett. (1995).