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Dense and sparse vertex connectivity in networks [article]

Djellabi Mehdi, Jouve Bertrand, Amblard Frédéric
2020 arXiv   pre-print
In the field of social networks at least, studies mainly address the detection and analysis of communities.  ...  We propose an algorithm, ItRich, to identify this type of nodes, based on the decomposition of a graph into successive, less and less dense, layers.  ...  network, and the vertex is connected to the network by preferential attachment.  ... 
arXiv:2006.05679v1 fatcat:dhy53p7cbjbdtpkkdrgdsef6xm

Graphons: A Nonparametric Method to Model, Estimate, and Design Algorithms for Massive Networks [article]

Christian Borgs, Jennifer T. Chayes
2017 arXiv   pre-print
Here we describe the development of the theory of graphons, for both dense and sparse networks, over the last decade.  ...  Finally, we show how to use graphons to estimate missing links in a sparse network, which has applications from estimating social and information networks in development economics, to rigorously and efficiently  ...  xed densities of each species of vertex, and xed probabilities that any two species connect to each other, including a xed probability of intra-species connection, which is in general di erent within each  ... 
arXiv:1706.01143v1 fatcat:qrycnxgnjzepjfr3kyyjbpilda

Dense graphs with scale-free feature [article]

Fei Ma, Xiaomin Wang, Ping Wang, Xudong Luo
2019 arXiv   pre-print
While the authors in Ref had already stated that all scale-free networks are sparse, there exist some real-world networks, for instance, social networks , urban networks , information networks , which  ...  By contrast, in this paper, we propose a novel framework for generating scale-free graphs with dense feature using two simple yet helpful operations, first-order subdivision and Line-operation, from graph  ...  Sparse models are of k → α in the limit of large graph size and the dense ones are of k = α where α is a constant. Obviously, all scale-free networks with γ in the range from 2 to 3 are sparse.  ... 
arXiv:1912.08923v1 fatcat:lvk667zf35bytmh4bv64jcw6sq

Globally Optimal Dense and Sparse Spanning Trees, and their Applications

Mustafa Ozen, Goran Lesaja, Hua Wang
2020 Statistics, Optimization and Information Computing  
Recently, a novel notion of dense ( sparse ) tree, and in particular spanning tree (DST and SST respectively), is introduced as the structure that have a large (small) number of subtrees, or small (large  ...  of the graph and/or network.  ...  We obtain the dense spanning tree in Fig 8B and the sparse spanning tree in Fig 8C.  ... 
doi:10.19139/soic-2310-5070-855 fatcat:bz27zce6x5bvzlqtirxcrmpxjy

The effect of the density of candidate roads on solutions in tactical forest planning

Nader Naderializadeh, Kevin A. Crowe
2018 Canadian Journal of Forest Research  
Acknowledgements 599 This research was funded by an NSERC Strategic Network grant on Value Chain 600 Optimization. We also thank Tomislav Sapic for his generous assistance in using GIS.  ...  Network representation of sixteen candidate road-links (arcs) Maps of a) a dense set, and b) a sparse set of candidate roads generated using an optimal road location model.  ...  a dense set of candidate roads. 579 Conclusions 580 In this paper, a set of three data sets was prepared in which a dense versus a sparse set 581 of candidate roads was generated in order that a  ... 
doi:10.1139/cjfr-2017-0176 fatcat:hvhq2khrevgp7i7cgdhhyrkczi

Virtual Network Embedding: A Hybrid Vertex Mapping Solution for Dynamic Resource Allocation

Adil Razzaq, Markus Hidell, Peter Sjödin
2012 Journal of Electrical and Computer Engineering  
Virtual network embedding (VNE) is a key area in network virtualization, and the overall purpose of VNE is to map virtual networks onto an underlying physical network referred to as a substrate.  ...  A virtual network (VN) can be described in terms of vertices (nodes) and edges (links) with certain resource requirements, and, to embed a VN, substrate resources are assigned to these vertices and edges  ...  In order to thoroughly investigate the impact of vertex mapping by any approach, evaluations are done by mapping sparsely and densely connected VNs on sparsely as well as densely connected substrate networks  ... 
doi:10.1155/2012/358647 fatcat:3edax2sqpzb6ha3qm775bcktxi

Globally optimal dense and sparse spanning trees, and their applications [article]

Mustafa Ozen, Goran Lesaja, Hua Wang
2020 arXiv   pre-print
Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the structure that have a large (small) number of subtrees, or small (large  ...  of the graph and/or network.  ...  When applied to a collaboration network with 379 nodes and 914 edges [23, 24] and a re-tweet network with 96 nodes and 117 edges [23, 25] in Fig 9, our method once again produces the dense and sparse  ... 
arXiv:2001.06958v1 fatcat:ib5we3juzbcb7c4h6yuupjx4ai

Optimization in complex networks [article]

R. Ferrer i Cancho, R. V. Sole
2001 arXiv   pre-print
, (c) star networks and (d) highly dense networks, apparently defining three major phases.  ...  Using an evolutionary algorithm involving minimization of link density and average distance, four major types of networks are encountered: (a) sparse exponential-like networks, (b) sparse scale-free networks  ...  This work was supported by (and started at) the Santa Fe Institute (RFC and RVS) and grants of the Generalitat de Catalunya (FI/2000-00393, RFC) and the CICYT (PB97-0693, RVS).  ... 
arXiv:cond-mat/0111222v1 fatcat:v3xwf3nc6ffz5cmuqtrvxohupe

Solving Statistical Mechanics on Sparse Graphs with Feedback Set Variational Autoregressive Networks [article]

Feng Pan, Pengfei Zhou, Hai-Jun Zhou, Pan Zhang
2020 arXiv   pre-print
It extracts a small Feedback Vertex Set (FVS) from the sparse graph, converting the sparse system to a much smaller system with many-body and dense interactions with an effective energy on every configuration  ...  On random graphs and real-world networks, our approach significantly outperforms the standard methods for sparse systems such as the belief-propagation algorithm; on structured sparse systems such as two-dimensional  ...  Here FVS is our approach while Dense represent densely connected VAN in [8] .  ... 
arXiv:1906.10935v2 fatcat:zt3notnp7fewtitf2pq2bat4oa

Dense networks that do not synchronize and sparse ones that do [article]

Alex Townsend, Michael Stillman, Steven H. Strogatz
2020 arXiv   pre-print
We also consider the opposite end of the connectivity spectrum, where the networks are sparse rather than dense.  ...  Thus, even for systems as simple as Kuramoto oscillators, much remains to be learned about dense networks that do not globally synchronize and sparse ones that do.  ...  FIG. 1 . 1 Dense circulant networks and sparse ones of size n = 8, 16, and 32. Panels (a)-(c) B. The Wiley-Strogatz-Girvan (WSG) network 9 .  ... 
arXiv:1906.10627v4 fatcat:zktlkcqve5csdp26diduvmcty4

Random clique covers for graphs with local density and global sparsity [article]

Sinead A. Williamson, Mauricio Tec
2019 arXiv   pre-print
Large real-world graphs tend to be sparse, but they often contain many densely connected subgraphs and exhibit high clustering coefficients.  ...  We develop a Bayesian nonparametric graph model based on random edge clique covers, and show that this model can capture power law degree distribution, global sparsity and non-vanishing local clustering  ...  For comparison, we also model the real-world graphs using the sparse graph model of Caron and Fox [2017] (labeled BNPgraph in  ... 
arXiv:1810.06738v2 fatcat:tmromhwxrfgtpczhqmpb47chfa

Optimization in Complex Networks [chapter]

Ramon Ferrer i Cancho, Ricard V. Solé
2003 Lecture Notes in Physics  
, (c) star networks and (d) highly dense networks, apparently defining three major phases.  ...  Using an evolutionary algorithm involving minimization of link density and average distance, four major types of networks are encountered: (a) sparse exponential-like networks, (b) sparse scale-free networks  ...  This work was supported by (and started at) the Santa Fe Institute (RFC and RVS) and grants of the Generalitat de Catalunya (FI/2000-00393, RFC) and the CICYT (PB97-0693, RVS).  ... 
doi:10.1007/978-3-540-44943-0_7 fatcat:6jdpq5fsuzdznh3wouksglj7zy

Dense Subgraph Extraction with Application to Community Detection

Jie Chen, Yousef Saad
2012 IEEE Transactions on Knowledge and Data Engineering  
The problem of identifying dense subgraphs helps analyze graph structures and complex networks and it is known to be challenging.  ...  Within the main applications of this "dense subgraph problem", the dense subgraphs are interpreted as communities, as in, e.g., social networks.  ...  The authors would like to thank Arindam Banerjee for introducing us to the dense subgraph problem and in particular for bringing to our attention the importance of finding a partial clustering of the graph  ... 
doi:10.1109/tkde.2010.271 fatcat:fv7s5ww6jvdgzg2xob7w5zwsg4

Robustness and Stability of Spin Glass Ground States to Perturbed Interactions [article]

Vaibhav Mohanty, Ard A. Louis
2020 arXiv   pre-print
For a sparse graph, a dense graph, and the fully connected Sherrington-Kirkpatrick model, we find relatively large sets of interactions that generate the same ground state.  ...  networks, as well as for models for genetic programming.  ...  ACKNOWLEDGEMENTS The authors would like to thank Sloan Nietert, Shuofeng Zhang, Wilber Lim, and Mehrana Nejad for helpful discussions. VM is supported by a Marshall Scholarship.  ... 
arXiv:2012.05437v1 fatcat:6r7lj2unm5butnphrryjhlq434

Distributed (Δ+1)-Coloring in Sublogarithmic Rounds [article]

David G. Harris, Johannes Schneider, Hsin-Hao Su
2018 arXiv   pre-print
We extend the set of distributed symmetry-breaking techniques by performing a decomposition of graphs into dense and sparse parts.  ...  We give a new randomized distributed algorithm for (Δ+1)-coloring in the LOCAL model, running in O(√(Δ))+ 2^O(√( n)) rounds in a graph of maximum degree Δ.  ...  We thank the anonymous reviewers for many helpful suggestions and comments.  ... 
arXiv:1603.01486v4 fatcat:esqg5746onfyjprhdl2lhoso6i
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