A new mechanism leading to scale-free networks is proposed in this Letter. It is shown that, in many cases of interest, the connectivity power-law behavior is neither related to dynamical properties nor to preferential attachment. Assigning a quenched fitness value x i to every vertex, and drawing links among vertices with a probability depending on the fitnesses of the two involved sites, gives rise to what we call a good-get-richer mechanism, in which sites with larger fitness are more likely to become hubs (i.e., to be highly connected).

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.

We develop an algorithm to detect community structure in complex networks. The algorithm is based on spectral methods and takes into account weights and links orientations. Since the method detects efficiently clustered nodes in large networks even when these are not sharply partitioned, it turns to be specially suitable to the analysis of social and information networks. We test the algorithm on a large-scale data-set from a psychological experiment of word association. In this case, it proves to be successful both in clustering words, and in uncovering mental association patterns.

We present here a study of the clustering and loops in the graph of Internet at the Autonomous Systems level. We show that, even if the whole structure is changing with time, the statistical distributions of loops of order 3,4,5 remain stable during the evolution. Moreover we will bring evidence that the Internet graphs show characteristic Markovian signatures, since its structure is very well described by the two point correlations between the degrees of the vertices. This indeed prove that the Internet belong to a class of network in which the two point correlation is sufficient to describe all their local (and thus global) structure. Data are also compared to present Internet models.PACS numbers: : 89.75. Hc, 89.75.Da, 89.75.Fb In the last five years the physics community has started to look at the Internet[1] as a beautiful example of a complex system with many degrees of freedom resulting in global scaling properties. The Internet in fact can be described as a network, with vertices and edges representing respectively Autonomous Systems (AS) and physical lines connecting them. Moreover it has been shown [2,3] that it belongs to the wide class of scale-free networks [4,5] emerging as the underline structure of a variety of real complex systems. But, beside the common scalefree connectivity distribution, what distinguish networks as different as the social networks of interactions and the technological networks as for example the Internet? Researchers have then started to characterize further the networks introducing different topological quantities beside the degree distribution exponent. Among those, the clustering coefficient C(k) [6] and the average nearest neighbor degree k nn (k) of a vertex as a function of its degree k [7,8]. In particular, measurements in Internet yield C(k) ∼ k −µ with µ ≃ 0.75 [9] and k nn ∼ k −ν with ν ≃ 0.5 [9]. A two-vertex degree anti-correlation has also been measured [10]. Accordingly, Internet is said to display disassortative mixing [11], because nodes prefer to be linked to peers with different degree rather than similar. This situation is opposed to that in social networks where we observe the so-called assortative mixing.Moreover, the modularity of the Internet due to the national patterns has been studied by measuring the slow decaying modes of a diffusion process defined on it [12]. Recently, more attention has been devoted to network motifs [13,14], i.e. subgraphs appearing with a frequency larger than that observed in maximally random graphs with the same degree sequence. Among those, the most natural class includes loops [15,16,17,18], closed paths of various lengths that visit each node only once. Loops are interesting because they account for the multiplicity of paths between any two nodes. Therefore, they encode the redundant information in the network structure.In this paper we will present the data of the scaling of the loops of length h ≤ 5 in the Internet graph and we will show that this scaling is very well reproduced by the two points correlation matrix ...

The interplay between topology and dynamics in complex networks is a fundamental but widely unexplored problem. Here, we study this phenomenon on a prototype model in which the network is shaped by a dynamical variable. We couple the dynamics of the Bak-Sneppen evolution model with the rules of the so-called fitness network model for establishing the topology of a network; each vertex is assigned a fitness, and the vertex with minimum fitness and its neighbours are updated in each iteration. At the same time, the links between the updated vertices and all other vertices are drawn anew with a fitness-dependent connection probability. We show analytically and numerically that the system self-organizes to a non-trivial state that differs from what is obtained when the two processes are decoupled. A power-law decay of dynamical and topological quantities above a threshold emerges spontaneously, as well as a feedback between different dynamical regimes and the underlying correlation and percolation properties of the network.Comment: Accepted version. Supplementary information at http://www.nature.com/nphys/journal/v3/n11/suppinfo/nphys729_S1.htm