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Agata Fronczak

Publications and source records attributed to Agata Fronczak.

7 recordsLinked to original sources
PubMed2006

Networks with given two-point correlations: hidden correlations from degree correlations.

This paper orders certain important issues related to both uncorrelated and correlated networks with hidden variables, in which hidden variables correspond to desired node degrees. In particular, we show that networks being uncorrelated at the hidden level are also lacking in correlations between node degrees. The observation supported by the depoissonization idea allows us to extract a distribution of hidden variables from a given node degree distribution. It completes the algorithm for generating uncorrelated networks that was suggested by other authors. In this paper we also carefully analyze the interplay between hidden attributes and node degrees. We show how to extract hidden correlations from degree correlations. Our derivations provide a mathematical background for the algorithm for generating correlated networks that was proposed by Boguñá and Pastor-Satorras.

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PubMed2006

Fluctuation-dissipation relations in complex networks.

In this paper, we study fluctuations over several ensembles of maximum-entropy random networks. We derive several fluctuation-dissipation relations characterizing the susceptibilities of different networks to changes in external fields. In the case of networks with a given degree sequence, we argue that the scale-free topologies of real-world networks may arise as a result of the self-organization of real systems into sparse structures with low susceptibility to random external disruptions. We also show that the ensembles of networks with a given degree sequence and networks characterized by two-point correlations are equivalent to random networks with hidden variables.

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PubMed2005

Universal scaling of distances in complex networks.

Universal scaling of distances between vertices of Erdos-Rényi random graphs, scale-free Barabási-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k(i) and k(j) equals to (l(ij)) = A - B log(k(i)k(j)). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree (k)nn calculated for the nearest neighbors and on network clustering coefficients.

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PubMed2004

Average path length in random networks.

Analytic solution for the average path length in a large class of uncorrelated random networks with hidden variables is found. We apply the approach to classical random graphs of Erdös and Rényi (ER), evolving networks introduced by Barabási and Albert as well as random networks with asymptotic scale-free connectivity distributions characterized by an arbitrary scaling exponent alpha>2. Our result for 2 infinity there is a saturation effect for the average path length.

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PubMed2004

Supremacy distribution in evolving networks.

We study a supremacy distribution in evolving Barabasi-Albert networks. The supremacy s(i) of a node i is defined as the total number of all nodes that are not older than i and can be linked to it by a directed path (including the node i ). The nodes form a basin connected to the node i as its in-component. For a network with a characteristic parameter m=1,2,3,... , the supremacy of an individual node increases with the network age as t((1+m)/2) in an appropriate scaling region. It follows that there is a relation s(k) approximately k(m+1) between a node degree k and its supremacy s , and the supremacy distribution P(s) scales as s(-1-2/(1+m)) . Analytic calculations basing on a continuum theory of supremacy evolution and on a corresponding rate equation have been confirmed by numerical simulations.

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PubMed2003

Mean-field theory for clustering coefficients in Barabási-Albert networks.

We applied a mean-field approach to study clustering coefficients in Barabási-Albert (BA) networks. We found that the local clustering in BA networks depends on the node degree. Analytic results have been compared to extensive numerical simulations finding a very good agreement for nodes with low degrees. Clustering coefficient of a whole network calculated from our approach perfectly fits numerical data.

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