Related papers: Higher order clustering coefficients in Barabasi-A…
The degree distribution, referred to as the delta-sequence of a network is studied. Using the non-normalized Lorenz curve, we apply a generalized form of the classical majorization partial order. Next, we introduce a new class of small…
The small-world property is known to have a profound effect on the navigation efficiency of complex networks [J. M. Kleinberg, Nature 406, 845 (2000)]. Accordingly, the proper addition of shortcuts to a regular substrate can lead to the…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
In this paper, we investigate the effect of local structures on network processes. We investigate a random graph model that incorporates local clique structures to deviate from the locally tree-like behavior of most standard random graph…
This paper presents a new definition of the community structure of a network, which takes also into account how communities are stratified. In particular, we extend the standard concept of clustering coefficient and provide the local…
Given a graph $G = (V,E)$, an $(\alpha, \beta)$-ruling set is a subset $S \subseteq V$ such that the distance between any two vertices in $S$ is at least $\alpha$, and the distance between any vertex in $V$ and the closest vertex in $S$ is…
In modern data center networks, thousands of hosts contend for shared link capacity; the scale of these systems makes centralized scheduling impractical. This article models such scheduling as a bipartite matching problem under…
The distribution of the ratios of nearest neighbor level spacings has become a popular indicator of spectral fluctuations in complex quantum systems like interacting many-body localized and thermalization phases, quantum chaotic systems,…
Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…
We study the behavior of the clustering coefficient in tagged networks. The rich variety of tags associated with the nodes in the studied systems provide additional information about the entities represented by the nodes which can be…
Among all characteristics exhibited by natural and man-made networks the small-world phenomenon is surely the most relevant and popular. But despite its significance, a reliable and comparable quantification of the question `how small is a…
In this work, we propose a new clustering algorithm to group nodes in networks based on second-order simplices (aka filled triangles) to leverage higher-order network interactions. We define a simplicial conductance function, which on…
We propose a model of network growth in which the network is co-evolving together with the dynamics of a quantum mechanical system, namely a quantum walk taking place over the network. The model naturally generalizes the Barab\'{a}si-Albert…
The statistical property of a growing scale-free network is studied based on an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett. 86, 5401 (2001)], with the additional constraints of forbidden of self-connection and…
In this letter, we propose a simple rule that generates scale-free networks with very large clustering coefficient and very small average distance. These networks are called {\bf Random Apollonian Networks}(RANs) as they can be considered…
An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modelling or block-clustering. The model is the stochastic blockmodel…
We find that a wide class of developing and decaying networks has scaling properties similar to those that were recently observed by Barab\'{a}si and Albert in the particular case of growing networks. The networks considered here evolve…
A useful property of a network that can be used to characterize many systems is the degree distribution. However, many complex networks exhibit higher--order degree correlations that must be studied through other means, such as clustering…
Performance of standard processes over large distributed networks typically scales with the size of the network. For example, in planar topologies where nodes communicate with their natural neighbors, the scaling factor is $O(n)$, where $n$…
We introduce a minimal network model which generates a modular structure in a self-organized way. To this end, we modify the Barabasi-Albert model into the one evolving under the principle of division and independence as well as growth and…