Scale-Free Networks

The paper analyses methodological issues concerning selection of indicators, making them scale-free and construction of composite indices within the framework of measuring human development. It reviews the existing literature in the area and highlights the key areas of concern from the viewpoint of methodology of aggregation. It discusses the implications of the assumptions underlying different techniques, currently being used in India, in the context of an empirical exercise of constructing an index of human development at state level. It examines the advantages and disadvantages of these techniques and proposes improvements therein for bringing them closer to empirical reality and thereby increasing their acceptability among the planners and policy-makers. The study suggests that exercises at determining the levels of human development at the state or district level by official agencies like the Planning Commission, concerned ministries or an international agency must enjoy large ...

While the majority of approaches to the characterization of complex networks has relied on measurements considering only the immediate neighborhood of each network node, valuable information about the network topological properties can be obtained by considering further neighborhoods. The current work considers the concept of virtual hierarchies established around each node and the respectively defined hierarchical node degree and clustering coefficient (introduced in cond-mat/0408076), complemented by new hierarchical measurements, in order to obtain a powerful set of topological features of complex networks. The interpretation of such measurements is discussed, including an analytical study of the hierarchical node degree for random networks, and the potential of the suggested measurements for the characterization of complex networks is illustrated with respect to simulations of random, scale-free and regular network models as well as real data (airports, proteins and word associations). The enhanced characterization of the connectivity provided by the set of hierarchical measurements also allows the use of agglomerative clustering methods in order to obtain taxonomies of relationships between nodes in a network, a possibility which is also illustrated in the current article.

... |EvalAi(Gk)-EvalAj(Gk)| is the similarity of the content evaluation in the contents category Gk between two agents Ai and Aj, - EvalAj(Gk) is the parameter defining ... 2 shows that, in the range of edge 16, the probability is P(k)～k-α ;-1.5<α<2.1, and that it is clearly a scale-free net-...

In the last years, complex networks have become an
increasingly relevant research topic due to the large
number of fields of application. Particularly, complex
networks are specially significant in the area of modern Online Social Networks (OSNs). OSNs are actually a challenge for complex network analysis, as
they present some characteristics that hinder topology processing. Concretely, social-networks volume
is exceedingly big, as they have a high number of
nodes and links. One of the most popular and influential OSN is Twitter. This article proves that twitter is
a complex network computing an estimated value of
luster coefficient, power law, and average path length.

We study structure, eigenvalue spectra and diffusion dynamics in a wide class of networks with subgraphs (modules) at mesoscopic scale. The networks are grown within the model with three parameters controlling the number of modules, their internal structure as scale-free and correlated subgraphs, and the topology of connecting network. Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic graphs and trees. The minimally connected nodes, clustering, and the average connectivity affect the central part of the spectrum. The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs. Such a peak does not occur in the case of topologically distinct tree-subgraphs connected on a tree. Whereas the associated eigenvectors remain localized on the subgraphs both in trees and cyclic graphs. We also find a characteristic pattern of periodic localization along the chains on the tree for the eigenvector components associated with the largest eigenvalue equal 2 of the Laplacian. We corroborate the results with simulations of the random walk on several types of networks. Our results for the distribution of return-time of the walk to the origin (autocorrelator) agree well with recent analytical solution for trees, and it appear to be independent on their mesoscopic and global structure. For the cyclic graphs we find new results with twice larger stretching exponent of the tail of the distribution, which is virtually independent on the size of cycles. The modularity and clustering contribute to a power-law decay at short return times.

El presente estudio además de analizar cuáles fueron las principales vías de aprovisionamiento de los productos de carácter suntuario más relevantes en los mercados romanos, pretende ofrecer al lector un nuevo escenario para el debate mediante la incorporación de las teorías de redes a un tema ya de por sí bastante prolífico: el comercio de productos orientales. Así, por primera vez, el uso de las crónicas chinas, junto con las fuentes clásicas (romanas), nos ha permitido comprobar
hasta qué punto existió similitud en los comentarios sobre las riquezas de la región que comprenden los territorios de Egipto y Próximo Oriente. Si a esta concomitancia le sumamos los resultados obtenidos por las teorías de redes, en particular las desarrolladas por Stanley Milgram en 1967, nos percatamos de la existencia de una serie de ciudades entre continentes que destacaron por su paso obligado, a modo de “superconectores” o hubs, como principales mercados suntuarios.

The paper discusses the role of networks in cognition on two levels: on the level of the organization of ideas, and on the level of interpersonal communication. Any interesting system of ideas forms a network: ideas presented in a linear order (the order forced upon us by verbal expression) will necessarily convey a distorted picture of the underlying patterns of thought. Networks of ideas typically consist of a great number of nodes with just a few links, and a small number of hubs with very many links; that is, they are, to employ Albert-László Barabási’s term, “scale-free.” Barabási fits into a specific tradition: Hungarians had an early influence on the philosophy of networks, and on the philosophy of communication as developed at Marshall McLuhan’s Toronto Circle. In fact, this was the circle in which certain Hungarian and Austrian ideas on mediated collective thinking first came together—a telling testimony to the conditions of disturbed communication and idiosyncratic networking typical of East-Central Europe, past and present. The nodes-and-hubs pattern is characteristic, too, of social networks, in particular of scholarly and scientific networks. The paper analyses the role of “invisible colleges”—informal groups of scientific elites through whom the communication of information both within a field and across fields is channelled. By way of conclusion the notion of a new type of personality, the “network individual,” is discussed: the network individual is the person reintegrated, after centuries of relative isolation induced by the printing press, into the collective thinking of society—the individual whose mind is manifestly mediated, once again, by the minds of those forming his/her smaller or larger community.

Esta presentación examina el surgimiento de la teoría de grafos, los desarrollos de la Escuela de Negocios de Harvard, los sociogramas de Jacob Lévy Moreno, los grafos de Bavelas en el MIT y la teoría de las redes sociales de la Escuela de Manchester en antropología, hasta los modelos de pequeños mundos (los “seis grados de separación”) de Milgram, Watts y Strogatz y las redes libres de escala de Barabási.
Los últimos desarrollos de la teoría de grafos y de la teoría de redes sociales complejas en particular ponen en tela de juicio infinidad de supuestos sobre la naturaleza de las redes en la vida real y sus estructuras estadísticas concomitantes, la “distribución normal” en particular. Gran parte de los procedimientos metodológicos usuales en la investigación socio-cultural, comenzando por el muestreo y la prueba estadística de la hipótesis nula, se revelan fallidos allí donde se manifiesta una distribución independiente de escala o ley de potencia.