NFO13018901 Intro Network science14307130355李婧雅 FIG. 1 square lattice network Picture one is the square lattice network with the structure N=LL. Square lattice network is the most common rule network. The degrees of all nodes in the network are even distribution. The characteristics of it are the small average length and big clustering coefficient In the picture, nodes are distributed orderly in the points of intersection and we give he corresponding coordinate(i,j(ij are both integers in the range of (1, L)to each of them 2.2.2 BA scale-free network Barabasi and albert finds that er random network and ws small-world network overlook two important characteristics of network in real life: growth and preferential attachment. In 1999, they set up the Ba scale-free network model, solving the problems we referred 2.2.2.1 two basic characteristics A. Growth: the scale of network is constantly growing, B. Preferential attachment: new nodes are more likely to connect with hub nodes which have higher degree. It's called"rich get richer 2.2.2.2 procedure of setting up A. In the beginning, there are mo nodes in the network. Every time adding a new node, connect the new one with the origin node in the network and generate m s(m≤m0) B. When connect the new node with the origin ones, the probability follows the rule p ∑ C It cant appear repeated connections in the network Follow the above rules to generate Ba scale-free network. When the number of nodes N>0, degree distribution follow the relation P(k)=2mk and the powerINFO130189.01 Intro Network Science 14307130355 李婧雅 4 FIG. 1 square lattice network Picture one is the square lattice network with the structure N=L*L. Square lattice network is the most common rule network. The degrees of all nodes in the network are even distribution. The characteristics of it are the small average length and big clustering coefficient. In the picture, nodes are distributed orderly in the points of intersection and we give the corresponding coordinate (i , j) (i,j are both integers in the range of (1,L)) to each of them. 2.2.2 BA scale-free network Barabási and Albert finds that ER random network and WS small-world network overlook two important characteristics of network in real life: growth and preferential attachment. In 1999, they set up the BA scale-free network model, solving the problems we referred. 2.2.2.1 two basic characteristics A. Growth: the scale of network is constantly growing; B. Preferential attachment: new nodes are more likely to connect with hub nodes which have higher degree. It’s called “rich get richer”. 2.2.2.2 procedure of setting up A. In the beginning, there are m0 nodes in the network. Every time adding a new node, connect the new one with the origin node in the network and generate m links( m≤ m0 ) B. When connect the new node with the origin ones, the probability follows the rule:   j i i k k p C. It can’t appear repeated connections in the network. Follow the above rules to generate BA scale-free network. When the number of nodes N   , degree distribution follow the relation  P k  m k 2 ( ) 2 and the power