【正文】 ge amount of works on the characterization of the topological properties of real works has motivated the need to construct graphs with power law degree distributions. Graphs with a powerlaw degree distribution can besimply obtained as a special case of the random graphs with a given degree distribution discussed in Section . We denote such graphs as static scalefree to distinguish them from models of evolving graphs that will be discussed in Section . Aiello et al. have studied a model that involves only two parameters, and , and that assigns uniform probability egree k given by N (k) = e k? [132]. We denote this model as G, since both the total number of nodes N and edges K are fully determined, once and are given. Notice that is the logarithm of the number of nodes with k = 1, while e/is the maximum degree of the graph. Aiello et al. have shown that the Molloy and Reed criterium predicts that G , has a giant ponent when c= . . . , and have proved that the second largest ponents are of size O(log N ) for 2 cand O(1) for 1 2, while the graph is almost surely connected for 0 1. By using Eq. (), Newman has calculated the clustering coef?cient for powerlaw degree distributions ?nding: C～N(3 ?7)/(?1). Thus, C tends to zero in large graphs with 7/3, while for 7/3, C increases with the system size, due to the fact that there can be, in average, more than one edge between two nodes sharing a mon neighbor [4]. Chung and Lu have studied the average distance in random graphs with a powerlaw degree distribution, proving that L scales as log N if 3. Conversely, if 2 3, L is O(log log N ), while the diameter is O(log N ) [125]. Similar results were obtained by Cohen and Havlin [133]. More recently, Chung et al. have shown that the spectrum of the adjacency matrix of random power law graphs follows a power law distribution, while the eigenvalues of the normalized Laplacian follow the semicircle law [134]. Several other recipes to construct static scalefree works, based on assuming that a node has some intrinsic properties, have been proposed in the physics munity. In the model by Goh et al. [42], each node i is assigned a weight (or ?tness) wi=i, where i =1, 2 , . . . , N is the node index and is a tunable parameter in [0, 1). Two different nodes, i and j , are selected with probabilities equal to the normalized weights wi /lwl and wj /lwl, respectively, and are connected if there is not already a link between them. The process is repeated until mN links are made in the system, so thatk = 2m. When = 0 one obtains a ER random graph. When = 0, the graph obtained has a power law degree distribution P (k) ～ k?with an exponen=1 + 1/. Thus, by varyingin [0, 1) one obtains an exponentin the range 2 ∞. The betweenness distribution follows a power law with an exponent = for any value of in the range 2 3 [42,45]. A similar ?tness model was studied by Caldarelli et al. [135]. The model starts with N isolated nodes, and associatesat every node i a ?tnessi, which is a real number taken from a ?tness distribution(). For every couple of nodes, i and j , a link is drawn with a probability f (i,j), with f being a symmetric function of its arguments. The model generates powerlaw P (k) for various ?tness distributions and attaching rules, while it gives ER random graph if f (i,j) = p? i, j. Recently, Masuda et al. focused on the threshold graph model which is a subclass of the previousmodel particularly suited to the analytical treatment. The connectivity betw een a pair of nodes in the model is determined by whether the sum of the ?tness of the pair exceeds a given threshold , namely f (i,j) = 1 ifi+j, and f (i,j) = 0 otherwise [136]. We ?nally mention gradient works, . directed graphs induced by local gradients of a scalar ?eld distributed on the nodes [137–139]. In the simplest model, Toroczkai and Bassler consider a given substrate work, S, and a nondegenerate scalar, hi, associated with each node i and describing the potential of the node. Then, the gradient work is constructed as the collection of directed links pointing from each node to whichever of its neighbors on has the highest potential [137]. It can be shown that gradient works consist only of trees. Furthermore, if the substrate work S is scalefree, and the scalars hi are ind ependent identically distributed random variables, then the associated gradient work is scalefree 3 and characterized by the same exponent. More interestingly, if S is a random graph (and hi are independent identically distributed random variables), then the gradient work is scale free with the indegree distribution P (kin) being a decreasing power law with an exponentin= 1 [137,138]. . Evolving scalefree works Static scalefree graphs are good models for all cases in which growth or aging processes do not play a dominant role in determining the structural properties of the work. Conversely, there are many examples of real works in which the structural changes are ruled by the dynamical evolution of the system. Here we discuss a class of models whose primary goal is to reproduce the growth processes taking place in real works: the rationale is that, by mimic kingthe dynamical mechanisms that assembled the work, one will be able to reproduce the topological properties of thesystem as we see them today. We concentrate primarily on the model of work growth proposed by Barab225。si–Albert (BA) model is a model of work growth inspired to the formation of the World Wide Web and is based on two basic ingre dients: growth and preferential attachment [93]. The basic idea is that in the World Wide Web, sites with high degrees acquire new links at higher rates than lowdegree nodes. More precisely, a undirectegraph GBA N,K is constructed as follows. Starting with m0isolated nodes, at each time step t = 1, 2, 3, . . . , N ? m0new node j w