Related papers: Algorithmic Complexity of Power Law Networks
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…
Besides the complexity in time or in number of messages, a common approach for analyzing distributed algorithms is to look at the assumptions they make on the underlying network. We investigate this question from the perspective of network…
Since its first use by Euler on the problem of the seven bridges of K\"onigsberg, graph theory has shown excellent abilities in solving and unveiling the properties of multiple discrete optimization problems. The study of the structure of…
This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. The manuscript covers in a simple way…
This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the…
Recent work on the structure of social networks and the internet has focussed attention on graphs with distributions of vertex degree that are significantly different from the Poisson degree distributions that have been widely studied in…
The present paper studies local distributed graph problems in highly dynamic networks. Communication and changes of the graph happen in synchronous rounds and our algorithms always, i.e., in every round, satisfy non-trivial guarantees, no…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
We study the family of network models derived by requiring the expected properties of a graph ensemble to match a given set of measurements of a real-world network, while maximizing the entropy of the ensemble. Models of this type play the…
Many communication and social networks have power-law link distributions, containing a few nodes which have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and…
Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. Moreover, many machine learning algorithms and…
Recent advances in dynamic graph processing have enabled the analysis of highly dynamic graphs with change at rates as high as millions of edge changes per second. Solutions in this domain, however, have been demonstrated only for…
In the last decades, the study of models for large real-world networks has been a very popular and active area of research. A reasonable model should not only replicate all the structural properties that are observed in real world networks…
Understanding the mathematical properties of graphs underling biological systems could give hints on the evolutionary mechanisms behind these structures. In this article we perform a complete statistical analysis over thousands of graphs…
In the field of complex networks, hypergraph models have so far received significantly less attention than graphs. However, many real-life networks feature multiary relations (co-authorship, protein reactions) may therefore be modeled way…
Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental distributed agreement problem. P2P networks are highly dynamic networks that experience…
It appeared recently that the underlying degree distribution of networks may play a crucial role concerning their robustness. Empiric and analytic results have been obtained, based on asymptotic and mean-field approximations. Previous work…
Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet…