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The scale of Internet is increasingly large by increasing demand and technology progress , its topology structure is becoming more and more complicated, the large-scale topology network research[2-4] for is apparently unsuited for the "blind" study only in the whole network .Not only the overall topology characteristics and its relation to the network are studied deeply, but also consider the method of division of the network with different coarse grained, relationship between structure characteristics and the overall network topology characteristics of coarse-grained network topology.
So between the nodes with the most possible edge numbers is , the ratio between the nodes to define the actual number of edges and the total possible number of edges E , it’s (2) The clustering coefficient of the whole network is the average clustering coefficient of all the nodes
b) higher-order metrics: such as local clustering coefficient, the number of core nodes and so on.
The number of kernel node reflects the depth of the number in the nucleus, nucleus chart reflects the hierarchy, the number of layers of nuclear number is greater the higher
· Betweenness Centrality: if take a net as a graph, is the collect of all nodes in the net. equation presents the distance of node and node], it is also the number of the shortest way which include the number of nodes。

The AFM result (see Fig.1(b) ) shows that grain is uniform and aligning.
Some subtle changes of XRD patterns can likewise be found in (110) and (211) directions, which are closely related to the grain size of FeAl films.
To this end, we refined the XRD results to gain FeAl lattice parameters and grain size.
After 128h vacuum heat treatment, the lattice constant increased to 2.911Å due to the existence of a large number of atomic vacancies.
As the treatment time goes on, the introduction of hydrogen leads to the lattice swelling and grain damage of the alloy thin films.

High temperature annealings promote matrix grain coarsening, and a concurrent hardness decrease.
longer milling times the carbide structure remained compatible with Fe7C3.After 50 hours milling the grain size (XRD) of copper reached 13 nm and the grain size of the carbide particles had a similar value, 11 nm.
These pictures were obtained in the backscattered electron mode (BSE), in order to evidence the contrast from the average atomic number from each phase.
Not even appreciable grain growth is detected at 600ºC, let alone recrystallization.
High resolution examination of grain boundary structure would be very enlightening in that respect.

Assuming all the grains are arranged in one circle and the grain shape is cone along normal direction, the action of a single grain in grinding is shown in Fig.3.
Fig.3 Action of a single grain in grinding Fig.4 Structure of elastic core clamper The tangential grinding force and the normal grinding force of a single grain may be expressed as[5-6] Where γ is half cone angle, ap is the cut depth, vw is the workpiece speed, vs is the wheel speed, r is the workpiece radius, R is the wheel radius, δ is the distance between grains, and ε is influence coefficient 0.2-0.5.
Therefore the total grinding force is where j is the number of active grains and can be expressed as where l is the contact length, and b is the workpiece width.

Tensile strength was studied to improve with increase in number of particles and decrease in size of particles but however, wear volume loss was found to decrease with particles[8], [9].
The reinforcement particles of and have occupied the grain boundaries of Al-Si eutectic grains.
ASTM E112-13 standard methods for determination of grain size were followed and the average grain size of the sample was estimated using intercept procedure.
The average grain size of the samples was estimated to be 35.97, 56.66 and 58.27 microns respectively.
The reinforcement particles of and was noticed to occupy the grain boundaries of Al-Si eutectic grains. 2.

In fact, the domain switching is strongly influenced by the grain size, the grain orientation and the scale size effects (the reduced thickness and the important surface versus volume ratio) [1, 2].
The finite element approximation is constructed by dividing the domain 0B into elementary domains 0 1 eln n e n B B = = = ∪ where eln is the total number of elements.
Many adaptations to the constitutive law will be considered in the future in order to take into account the special effects (grain size and scale effects) inherent to thin ferroelectric films.
Kamel, G. de With, Grain size effect on the poling of soft Pb(Zr,Ti)O3 ferroelectric ceramics, J.
Chen, Effect of grain orientation and grain size on ferroelectric domain switching and evolution: Phase field simulations, Acta Materialia [3] M.Elhadrouz, T.

Introduction Lead zirconate titanate, Pb(Zr,Ti)O3 or PZT, is a well known piezoelectric that has been widely employed in a large number of sensing and actuating devices.
Grain size was determined from SEM micrographs by a linear intercept method.
It can be seen from Fig. 2 that Al ions are mainly accumulated at the grain boundaries [8].
Atkim et al. [9] reported that dopant ions were concentrated at grain boundaries and took excess impurities by diffusion when grain boundaries moved, which in turn reduced grain boundary mobility and size.
The micrographs also show that the grain size of the ceramics varies considerably.

Bienert p. first proposed the model of cutting stone material by a single grain diamond.
The cleavage plane, grain boundary and cracks of the granite are the place where the granite thin slab fractured in.
As the quartz show a typical brittle feature, when granite thin slab is subject to certain pressure, cracks will appear near them in a large number, but the similar phenomenon is difficult to be observed in the feldspar.
The internal factors are native cracks, micro voids, grain boundaries of the granite thin slab, etc
There are internal defects in the granite, such as native cracks, micro voids and grain boundaries.

Calcium (Ca) is one of a small number of alloying elements that can be included in implants.
Binary Mg-Ca alloy has better corrosion resistance as the accession of Calcium element, causing grain refinement.
The extra amount of Ca precipitates as Mg2Ca phases on grain boundaries and sporadically inside the grains (Fig. 1).
There were more nuclei as the existence of Mg2Ca and also it (on grain boundaries) restricted the growth of newly nucleated grains, resulting the decrease of grain size.
Followings were the conclusions of this experimental study: The adding of calcium element could refine the grain size in some extent as observed by electron microscope.

Microstructures were observed and average grain sizes were estimated using a scanning electron microscope (SEM; Hitachi S-2400).
While the average grain sizes increased slightly with increasing CeO2 contents up to 0.1wt%, the grain size abruptly increased over 0.1wt%.
In case of PZ-PT(PZT) system, the values of electromechanical coupling factor (kp), relative dielectric constant (K33 T ), were reported to show the maximum values in the morphtropic phase boundary�(MPB) region of tetragonal and rhombohedral phase because the numbers of spontaneous polarizations were maximized in that region [10].
Microstructures were fairly uniform with slightly growing average grain size.
The grain size in microstructure might be attributed to the increasing tetragonality which increases internal stress.