Local rewiring rules for evolving complex networks

ERC is grateful for the nancial support of the EPSRC

Emergence of Global Preferential Attachment From Local Interaction

Global degree/strength based preferential attachment is widely used as an evolution mechanism of networks. But it is hard to believe that any individual can get global information and shape the network architecture based on it. In this paper, it is found that the global preferential attachment emerges from the local interaction models, including distance-dependent preferential attachment (DDPA) evolving model of weighted networks(M. Li et al, New Journal of Physics 8 (2006) 72), acquaintance network model(J. Davidsen et al, Phys. Rev. Lett. 88 (2002) 128701) and connecting nearest-neighbor(CNN) model(A. Vazquez, Phys. Rev. E 67 (2003) 056104). For DDPA model and CNN model, the attachment rate depends linearly on the degree or strength, while for acquaintance network model, the dependence follows a sublinear power law. It implies that for the evolution of social networks, local contact could be more fundamental than the presumed global preferential attachment. This is onsistent with the result observed in the evolution of empirical email networks.Comment: 9 pages, 5 figure

A relational approach to knowledge spillovers in biotech. Network structures as drivers of inter-organizational citation patterns

In this paper, we analyze the geography of knowledge spillovers in biotech by investigating the way in which knowledge ties are organized. Following a relational account on knowledge spillovers, we depict knowledge networks as complex evolving structures that build on pre-existing knowledge and previously formed ties. In economic geography, there is still little understanding of how structural network forces (like preferential attachment and closure) shape the structure and formation of knowledge spillover networks in space. Our study investigates the knowledge spillover networks of biotech firms by means of inter-organizational citation patterns based on USPTO biotech patents in the years 2008-2010. Using a Stochastic Actor-Oriented Model (SAOM), we explain the driving forces behind the decision of actors to cite patents produced by other actors. Doing so, we address directly the endogenous forces of knowledge dynamics.knowledge spillovers, network structure, patent citations, biotech, proximity

The Fractional Preferential Attachment Scale-Free Network Model

Many networks generated by nature have two generic properties: they are formed in the process of {preferential attachment} and they are scale-free. Considering these features, by interfering with mechanism of the {preferential attachment}, we propose a generalisation of the Barab\'asi--Albert model---the 'Fractional Preferential Attachment' (FPA) scale-free network model---that generates networks with time-independent degree distributions $p(k)\sim k^{-\gamma}$ with degree exponent $2<\gamma\leq3$ (where $\gamma=3$ corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the $f$ parameter, where $f \in (0,1\rangle$. Depending on the different values of $f$ parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on $f$, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that $f$ parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of $f$, FPA networks are not fractal.Comment: 16 pages, 6 figure

Tunable and Growing Network Generation Model with Community Structures

Recent years have seen a growing interest in the modeling and simulation of social networks to understand several social phenomena. Two important classes of networks, small world and scale free networks have gained a lot of research interest. Another important characteristic of social networks is the presence of community structures. Many social processes such as information diffusion and disease epidemics depend on the presence of community structures making it an important property for network generation models to be incorporated. In this paper, we present a tunable and growing network generation model with small world and scale free properties as well as the presence of community structures. The major contribution of this model is that the communities thus created satisfy three important structural properties: connectivity within each community follows power-law, communities have high clustering coefficient and hierarchical community structures are present in the networks generated using the proposed model. Furthermore, the model is highly robust and capable of producing networks with a number of different topological characteristics varying clustering coefficient and inter-cluster edges. Our simulation results show that the model produces small world and scale free networks along with the presence of communities depicting real world societies and social networks.Comment: Social Computing and Its Applications, SCA 13, Karlsruhe : Germany (2013

Mean-field theory for scale-free random networks

Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information is available display scale-free features. Here we study the scaling properties of the recently introduced scale-free model, that can account for the observed power-law distribution of the connectivities. We develop a mean-field method to predict the growth dynamics of the individual vertices, and use this to calculate analytically the connectivity distribution and the scaling exponents. The mean-field method can be used to address the properties of two variants of the scale-free model, that do not display power-law scaling.Comment: 19 pages, 6 figure

Random acyclic networks

Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the model's properties, including connection probabilities and component sizes, as well as a fast algorithm for simulating the model on a computer. We compare the predictions of the model to a real-world network of citations between physics papers and find surprisingly good agreement, suggesting that the structure of the real network may be quite well described by the random graph.Comment: 4 pages, 2 figure

Inferring Network Mechanisms: The Drosophila melanogaster Protein Interaction Network

Naturally occurring networks exhibit quantitative features revealing underlying growth mechanisms. Numerous network mechanisms have recently been proposed to reproduce specific properties such as degree distributions or clustering coefficients. We present a method for inferring the mechanism most accurately capturing a given network topology, exploiting discriminative tools from machine learning. The Drosophila melanogaster protein network is confidently and robustly (to noise and training data subsampling) classified as a duplication-mutation-complementation network over preferential attachment, small-world, and other duplication-mutation mechanisms. Systematic classification, rather than statistical study of specific properties, provides a discriminative approach to understand the design of complex networks.Comment: 19 pages, 5 figure