Abstract:
The Saccharomyces cerevisiae protein-protein interaction map, as well as many natural and man-made networks, shares the scale-free topology. The preferential attachment model was suggested as a generic network evolution model that yields this universal topology. However, it is not clear that the model assumptions hold for the protein interaction network. Using a cross genome comparison we show that (a) the older a protein, the better connected it is, and (b) The number of interactions a protein gains during its evolution is proportional to its connectivity. Therefore, preferential attachment governs the protein network evolution. The evolutionary mechanism leading to such preference and some implications are discussed.

Abstract:
Relevance and importance are the main factors when humans build network connections. We propose an evolutionary network model based on preferential attachment(PA) considering these factors. We analyze and compute several important features of the network class generated by this algorithm including scale free degree distribution, high clustering coefficient, small world property and core-periphery structure. We then compare this model with other network models and empirical data such as inter-city road transportation and air traffic networks.

Abstract:
The classical preferential attachment model is sensitive to the choice of the initial configuration of the network. As the number of initial nodes and their degree grow, so does the time needed for an equilibrium degree distribution to be established. We study this phenomenon, provide estimates of the equilibration time, and characterize the degree distribution cutoff observed at finite times. When the initial network is dense and exceeds a certain small size, there is no equilibration and a suitable statistical test can always discern the produced degree distribution from the equilibrium one. As a by-product, the weighted Kolmogorov-Smirnov statistic is demonstrated to be more suitable for statistical analysis of power-law distributions with cutoff when the data is ample.

Abstract:
In the advent of the Internet, web-mediated social networking has become of great influence to Filipinos. Networking sites such as Friendster, YouTube, FaceBook and MySpace are among the most well known sites on the Internet. These sites provide a wide range of services to users from different parts of the world, such as connecting and finding people, as well as, sharing and organizing contents. The popularity and accessibility of these sites enable information to be available. These allow people to analyze and study the characteristics of the population of online social networks. In this study, we developed a computer program to analyze the structural dynamics of a locally popular social networking site: The Friendster Network. Understanding the structural dynamics of a virtual community has many implications, such as finding an improvement on the current networking system, among others. Based on our analysis, we found out that users of the site exhibit preferential attachment to users with high number of friends.

Abstract:
Preferential attachment (PA) models of network structure are widely used due to their explanatory power and conceptual simplicity. PA models are able to account for the scale-free degree distributions observed in many real-world large networks through the remarkably simple mechanism of sequentially introducing nodes that attach preferentially to high-degree nodes. The ability to efficiently generate instances from PA models is a key asset in understanding both the models themselves and the real networks that they represent. Surprisingly, little attention has been paid to the problem of efficient instance generation. In this paper, we show that the complexity of generating network instances from a PA model depends on the preference function of the model, provide efficient data structures that work under any preference function, and present empirical results from an implementation based on these data structures. We demonstrate that, by indexing growing networks with a simple augmented heap, we can implement a network generator which scales many orders of magnitude beyond existing capabilities ($10^6$ -- $10^8$ nodes). We show the utility of an efficient and general PA network generator by investigating the consequences of varying the preference functions of an existing model. We also provide "quicknet", a freely-available open-source implementation of the methods described in this work.

Abstract:
We investigate a class of network growth rules that are based on a redirection algorithm wherein new nodes are added to a network by linking to a randomly chosen target node with some probability 1-r or linking to the parent node of the target node with probability r. For fixed 0

Abstract:
This paper describes the relationship between trading network and WWW network from preferential attachment mechanism perspective. This mechanism is known to be the underlying principle in the network evolution and has been incorporated to formulate two famous web pages ranking algorithms, PageRank and HITS. We point out the differences between trading network and WWW network in this mechanism, derive the formulation of HITS-based ranking algorithm for trading network as a direct consequence of the differences, and apply the same framework when deriving the formulation back to the HITS formulation that turns to become a technique to accelerate its convergences.

Abstract:
We propose a simple preferential attachment model of growing network using the complementary probability of Barab\'asi-Albert (BA) model, i.e., $\Pi(k_i) \propto 1-\frac{k_i}{\sum_j k_j}$. In this network, new nodes are preferentially attached to not well connected nodes. Numerical simulations, in perfect agreement with the master equation solution, give an exponential degree distribution. This suggests that the power law degree distribution is a consequence of preferential attachment probability together with "rich get richer" phenomena. We also calculate the average degree of a target node at time t $()$ and its fluctuations, to have a better view of the microscopic evolution of the network, and we also compare the results with BA model.

Abstract:
We study a model for the evolution of chemical species under a combination of population dynamics on a short time scale and a selection mechanism on a longer time scale. Least fit nodes are replaced by new nodes whose links are attached to the nodes of the given network via preferential attachment. In contrast to a random attachment of newly incoming nodes that was used in previous work, this preferential attachment mechanism accelerates the generation of a so-called autocatalytic set after a start from a random geometry and the growth of this structure until it saturates in a stationary phase in which the whole system is an autocatalytic set. Moreover, the system in the stationary phase becomes much more stable against crashes in the population size as compared to random attachment. We explain in detail in terms of graph theoretical notions which structure of the resulting network is responsible for this stability. Essentially it is a very dense core with many loops and less nodes playing the role of a keystone that prevents the system against crashes almost completely.

Abstract:
We study the growth of a directed transportation network, such as a food web, in which links carry resources. We propose a growth process in which new nodes (or species) preferentially attach to existing nodes with high indegree (in food-web language, number of prey) and low outdegree (or number of predators). This scheme, which we call inverse preferential attachment, is intended to maximize the amount of resources available to each new node. We show that the outdegree (predator) distribution decays at least exponentially fast for large outdegree and is continuously tunable between an exponential distribution and a delta function. The indegree (prey) distribution is poissonian in the large-network limit.