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Networks describe a variety of interacting complex systems in social science, biology and information technology. Usually the nodes of real networks are identified not only by their connections but also by some other characteristics. Examples of characteristics of nodes can be age, gender or nationality of a person in a social network, the abundance of proteins in the cell taking part in a protein-interaction networks or the geographical position of airports that are connected by directed flights. Integrating the information on the connections of each node with the information about its characteristics is crucial to discriminating between the essential and negligible characteristics of nodes for the structure of the network. In this paper we propose a general indicator, based on entropy measures, to quantify the dependence of a networks structure on a given set of features. We apply this method to social networks of friendships in US schools, to the protein-interaction network of Saccharomyces cerevisiae and to the US airport network, showing that the proposed measure provides information which complements other known measures.
Estimating the probabilities of linkages in a network has gained increasing interest in recent years. One popular model for network analysis is the exchangeable graph model (ExGM) characterized by a two-dimensional function known as a graphon. Estima
In this paper, we perform the initial and comprehensive study on the problem of measuring node relevance on signed social networks. We design numerous relevance measurements for signed social networks from both local and global perspectives and inves
This paper re-introduces the network reliability polynomial - introduced by Moore and Shannon in 1956 -- for studying the effect of network structure on the spread of diseases. We exhibit a representation of the polynomial that is well-suited for est
We present a new layout algorithm for complex networks that combines a multi-scale approach for community detection with a standard force-directed design. Since community detection is computationally cheap, we can exploit the multi-scale approach to
Spectral analysis has been successfully applied at the detection of community structure of networks, respectively being based on the adjacency matrix, the standard Laplacian matrix, the normalized Laplacian matrix, the modularity matrix, the correlat