Growing networks with two vertex types

Growing networks are introduced in which the vertices are allocated one of two possible growth rates; type A with probability p(t), or type B with probability 1−p(t). We investigate the networks using rate equations to obtain their degree distributions. In the first model (I), the network is constructed by connecting an arriving vertex to either a type A vertex of degree k with rate μk, where μ0, or to a type B vertex of degree k with rate k. We study several p(t), starting with p(t) as a constant and then considering networks where p(t) depends on network parameters that change with time. We find the degree distributions to be power laws with exponents mostly in the range 2γ3. In the second model (II), the network is constructed in the same way but with growth rate k for type A vertices and 1 for type B vertices. We analyse the case p(t)=c, where 0c1 is a constant, and again find a power-law degree distribution with an exponent 2γ3

Map equation for link community

Community structure exists in many real-world networks and has been reported being related to several functional properties of the networks. The conventional approach was partitioning nodes into communities, while some recent studies start partitioning links instead of nodes to find overlapping communities of nodes efficiently. We extended the map equation method, which was originally developed for node communities, to find link communities in networks. This method is tested on various kinds of networks and compared with the metadata of the networks, and the results show that our method can identify the overlapping role of nodes effectively. The advantage of this method is that the node community scheme and link community scheme can be compared quantitatively by measuring the unknown information left in the networks besides the community structure. It can be used to decide quantitatively whether or not the link community scheme should be used instead of the node community scheme. Furthermore, this method can be easily extended to the directed and weighted networks since it is based on the random walk.Comment: 9 pages,5 figure

Questions in, Knowledge iN?: A study of Naver’s question answering community

Large general-purposed community question-answering sites are becoming popular as a new venue for generating knowledge and helping users in their information needs. In this paper we analyze the characteristics of knowledge generation and user participation behavior in the largest question-answering online community in South Korea, Naver Knowledge–iN. We collected and analyzed over 2.6 million question/answer pairs from fifteen categories between 2002 and 2007, and have interviewed twenty six users to gain insights into their motivations, roles, usage and expertise. We find altruism, learning, and competency are frequent motivations for top answerers to participate, but that participation is often highly intermittent. Using a simple measure of user performance, we find that higher levels of participation correlate with better performance. We also observe that users are motivated in part through a point system to build a comprehensive knowledge database. These and other insights have significant implications for future knowledge generating online communities

The Power (Law) of Indian Markets: Analysing NSE and BSE trading statistics

The nature of fluctuations in the Indian financial market is analyzed in this paper. We have looked at the price returns of individual stocks, with tick-by-tick data from the National Stock Exchange (NSE) and daily closing price data from both NSE and the Bombay Stock Exchange (BSE), the two largest exchanges in India. We find that the price returns in Indian markets follow a fat-tailed cumulative distribution, consistent with a power law having exponent $\alpha \sim 3$, similar to that observed in developed markets. However, the distributions of trading volume and the number of trades have a different nature than that seen in the New York Stock Exchange (NYSE). Further, the price movement of different stocks are highly correlated in Indian markets.Comment: 10 pages, 7 figures, to appear in Proceedings of International Workshop on "Econophysics of Stock Markets and Minority Games" (Econophys-Kolkata II), Feb 14-17, 200

Scatter networks: a new approach for analysing information scatter

Information on any given topic is often scattered across the Web. Previously this scatter has been characterized through the inequality of distribution of facts (i.e. pieces of information) across webpages. Such an approach conceals how specific facts (e.g. rare facts) occur in specific types of pages (e.g. fact-rich pages). To reveal such regularities, we construct bipartite networks, consisting of two types of vertices: the facts contained in webpages and the webpages themselves. Such a representation enables the application of a series of network analysis techniques, revealing structural features such as connectivity, robustness and clustering. Not only does network analysis yield new insights into information scatter, but we also illustrate the benefit of applying new and existing analysis techniques directly to a bipartite network as opposed to its one-mode projection. We discuss the implications of each network feature to the users’ ability to find comprehensive information online. Finally, we compare the bipartite graph structure of webpages and facts with the hyperlink structure between the webpages.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/58170/2/njp7_7_231.pd

Vertex Intrinsic Fitness: How to Produce Arbitrary Scale-Free Networks

We study a recent model of random networks based on the presence of an intrinsic character of the vertices called fitness. The vertices fitnesses are drawn from a given probability distribution density. The edges between pair of vertices are drawn according to a linking probability function depending on the fitnesses of the two vertices involved. We study here different choices for the probability distribution densities and the linking functions. We find that, irrespective of the particular choices, the generation of scale-free networks is straightforward. We then derive the general conditions under which scale-free behavior appears. This model could then represent a possible explanation for the ubiquity and robustness of such structures.Comment: 4 pages, 3 figures, RevTe

Statistical Inference in a Directed Network Model with Covariates

Networks are often characterized by node heterogeneity for which nodes exhibit different degrees of interaction and link homophily for which nodes sharing common features tend to associate with each other. In this paper, we propose a new directed network model to capture the former via node-specific parametrization and the latter by incorporating covariates. In particular, this model quantifies the extent of heterogeneity in terms of outgoingness and incomingness of each node by different parameters, thus allowing the number of heterogeneity parameters to be twice the number of nodes. We study the maximum likelihood estimation of the model and establish the uniform consistency and asymptotic normality of the resulting estimators. Numerical studies demonstrate our theoretical findings and a data analysis confirms the usefulness of our model.Comment: 29 pages. minor revisio

Perturbation: the Catastrophe Causer in Scale-Free Networks

A new model about cascading occurrences caused by perturbation is established to search after the mechanism because of which catastrophes in networks occur. We investigate the avalanche dynamics of our model on 2-dimension Euclidean lattices and scale-free networks and find out the avalanche dynamic behaviors is very sensitive to the topological structure of networks. The experiments show that the catastrophes occur much more frequently in scale-free networks than in Euclidean lattices and the greatest catastrophe in scale-free networks is much more serious than that in Euclidean lattices. Further more, we have studied how to reduce the catastrophes' degree, and have schemed out an effective strategy, called targeted safeguard-strategy for scale-free networks.Comment: 4 pages, 6 eps figure

Bose-Einstein condensation in complex networks

The evolution of many complex systems, including the world wide web, business and citation networks is encoded in the dynamic web describing the interactions between the system's constituents. Despite their irreversible and non-equilibrium nature these networks follow Bose statistics and can undergo Bose-Einstein condensation. Addressing the dynamical properties of these non-equilibrium systems within the framework of equilibrium quantum gases predicts that the 'first-mover-advantage', 'fit-get-rich' and 'winner-takes-all' phenomena observed in competitive systems are thermodynamically distinct phases of the underlying evolving networks