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Locally C6 graphs are clique divergent

2000
*
Discrete Mathematics
*

We prove that all

doi:10.1016/s0012-365x(99)00233-2
fatcat:vvjpwiucjjfklf4rdbdrp7v7y4
*locally**C6**graphs**are*k-*divergent*and that the diameters of the iterated*clique**graphs*also tend to inÿnity with n while the sizes of the*cliques*remain bounded. ... A*graph*G is said to be k-*divergent*if |V (k n G)| tends to inÿnity with n. A*graph*is*locally**C6*if the neighbours of any given vertex induce an hexagon. ... In [9] we studied a family {G(r; s) | r; s¿4} of*locally*C 6*graphs*and we proved that they*are*k-*divergent*. ...##
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Clique divergent graphs with unbounded sequence of diameters

1999
*
Discrete Mathematics
*

The iterated

doi:10.1016/s0012-365x(99)90105-x
fatcat:cbfmrnr43napdhhm6vgcbovg6u
*clique**graphs*k"G*are*defined by k°G = G and k ~+ I G --kk"G A*graph*G is said to be k-*divergent*if [V(k"G)I tends to infinity with n. ... We provide examples of k-*divergent**graphs*such that the diameters of the iterated*clique**graphs*also tend to infinity with n. ... The question was raised in [19] whether k-*divergence*implies ~ok-*divergence*. This turns out to be false, since the*graphs*G(r,s)*are*k-*divergent*but they*are*cok-bounded. ...##
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Unsupervised analysis of activity sequences using event-motifs

2006
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Proceedings of the 4th ACM international workshop on Video surveillance and sensor networks - VSSN '06
*

Finally, we propose a method to automatically detect subsequences of events that

doi:10.1145/1178782.1178794
fatcat:lynftlpb3zbifacww4a3njwbkm
*are**locally*atypical in a structural sense. ... Results over extensive data-sets, collected from multiple sensor-rich environments*are*presented, to show the competence and scalability of the proposed framework. ... maximal*cliques*(with nodes ≥ 3) in the*graph*. ...##
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A Transcriptome Community-and-Module Approach of the Human Mesoconnectome

2021
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Entropy
*

*Graph*analysis allows exploring transcriptome compartments such as communities and modules for brain mesostructures. ... An approach to exploring those brain compartments is through

*graph*analysis, particularly through the

*graph*mesostructures, such as

*cliques*, communities, and modules. ... While the former indicates that some functions

*are*more related to general brain tissue architecture, the latter suggests interacting gene communities whose functions perform more

*local*endeavors. ...

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IBIA: Bayesian Inference via Incremental Build-Infer-Approximate operations on Clique Trees
[article]

2022
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arXiv
*
pre-print

Nodes

arXiv:2202.12003v1
fatcat:kl37t4gg2bd5tfy7dil6d3kcgq
*are*added to the CT as long as the sizes*are*within a user-specified*clique*size constraint. ... In the build stage of this approach, bounded-*clique*size partitions*are*obtained by building the*clique*tree (CT) incrementally. ...*Cliques*in this adjacency set*are*reconnected to*cliques*in ST that contain the corresponding sepset in the input CTF. For the example, the modified CT is shown in Figure 4d . ...##
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Landmarks Augmentation with Manifold-Barycentric Oversampling
[article]

2021
*
arXiv
*
pre-print

The proposed algorithm finds

arXiv:2104.00925v2
fatcat:ucwztbpbnjhglpdszccw6gnxvm
*cliques*in the nearest-neighbors*graph*and, at each sampling iteration, randomly draws one*clique*to compute the Wasserstein barycenter with random uniform weights. ... In practice, we consider the*clique*projection, all distances to the projection point*are*reduced. complex of the k-NN neighborhood*graph*. ... Then, one projects the internal*graph*, that is a k-simplex σ corresponds a*clique*in the ε- point into the nearest point of the k-polyhedron. With this neighborhood*graph*. ...##
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Variational Approximations between Mean Field Theory and the Junction Tree Algorithm
[article]

2013
*
arXiv
*
pre-print

We also show how the method fits into some other variational approximations that

arXiv:1301.3901v1
fatcat:hwcooxop7bgx3fobwznhkxczpe
*are*currently popular. ... This includes undirected*graphs*, directed acyclic*graphs*and junction trees. We derive generalized mean field equations to optimize the cluster potentials. ... Numer ical optimisation of .C( Q, �) = (log Q) -[ ( Q, �) with respect to Q and � leads to*local*minimum of an upper bound of the KL-*divergence*. ...##
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Chromatic transitions in the emergence of syntax networks

2018
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Royal Society Open Science
*

In particular, rapid transitions seem to occur as children reach the age of two, which seems to separate a two-word, tree-like network of syntactic relations among words from the scale-free

doi:10.1098/rsos.181286
pmid:30662738
pmcid:PMC6304139
fatcat:olpfdqej5nadlntn3kxlxpwz5u
*graphs*associated ... At a more general level, we observe that the chromatic classes define independent regions of the*graph*, and thus, can be interpreted as the footprints of incompatibility relations, somewhat as opposed ... These heterogenous networks cannot have a stable value of the chromatic number because their*clique*number (2.11)*diverges*with the*graph*size, even at constant kkl [29] . ...##
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Semantic Divergence Based Evaluation of Web Service Communities

2016
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2016 IEEE International Conference on Services Computing (SCC)
*

To achieve this goal we consider a probabilistic topic based approach to define a new measure called semantic

doi:10.1109/scc.2016.101
dblp:conf/IEEEscc/NaimAQD16
fatcat:npufrbqrhzgu7ictbipuottunq
*divergence*of communities. ... The essential idea is to prevent the premature condensation into few large communities. • greedy*clique*expansion (GCE) [21] works by first detecting a set of seeds in a*graph*G, then expanding these ... For example, communities rank of those detected by CMN is C3, C1, C2, whereas those detected by Louvain algorithm*are*ranked as follows : C7, C3,*C6*, C5, C4, C2, C1, C8. ...##
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Preserving Minority Structures in Graph Sampling
[article]

2020
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arXiv
*
pre-print

By comprehensively analyzing the literature on

arXiv:2009.02498v2
fatcat:uzj6thjf2nbwnjqrgrewxs6zca
*graph*sampling, we assume that existing algorithms cannot effectively preserve minority structures that*are*rare and small in a*graph*but*are*very important ... Sampling is a widely used*graph*reduction technique to accelerate*graph*computations and simplify*graph*visualizations. ... The remaining four SOI types, namely, small*cliques*far away from*graph*main bodies (FC), community overlapping structure (CSoverlapping),*local*high degree structure (HD-*local*), and isolated structure ...##
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Exploring complex networks

2001
*
Nature
*

If Q < 0, the

doi:10.1038/35065725
pmid:11258382
fatcat:wv7tm56dpjed3bvr2tyvs7yqnu
*graph*consists of many small components. The average component size*diverges*as Q→0 from below, and a giant component exists for Q > 0. ... , forming*cliques*. ...##
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Specificity determinants and diversification of the Brassica self-incompatibility pollen ligand

2003
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Proceedings of the National Academy of Sciences of the United States of America
*

Asterisks indicate the binding of wild-type SCR 6 to eSRK6 and of wild-type SCR13 to eSRK13 where values equal 1 and

doi:10.1073/pnas.2637116100
pmid:14694189
pmcid:PMC327116
fatcat:bm7i3va755burptule5dap7g74
*are*therefore not visible on the*graph*. ... In SCR, however, sequence comparisons*are*of little value for predicting the variant specificity determinants because all regions of the protein*are*highly*diverged*. ...##
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The complexity of pure Nash equilibria

2004
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Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04
*

We investigate from the computational viewpoint multi-player games that

doi:10.1145/1007352.1007445
dblp:conf/stoc/FabrikantPT04
fatcat:iolkx27lf5ebplvjx7igubyuau
*are*guaranteed to have pure Nash equilibria. ... PLS-completeness results*are*proved in terms of PLS reductions, providing also a mapping from*local*optima of the target problem to*local*optima of the original. ... Suppose then that we*are*given, besides F , this set of 2|X| lists, call them L. The witness*graph*W G(F, L) is a directed*graph*(V, EL), whose edges*are*defined as follows: for every variable xt) . ...##
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Classifying call profiles in large-scale mobile traffic datasets

2014
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IEEE INFOCOM 2014 - IEEE Conference on Computer Communications
*

Cellular communications

doi:10.1109/infocom.2014.6848119
dblp:conf/infocom/NaboulsiSF14
fatcat:ctygxtdx2vcopjoudcpsi5maza
*are*undergoing significant evolutions in order to accommodate the load generated by increasingly pervasive smart mobile devices. ... Other snapshots*diverge*from the typical behavior by joining minor clusters. These snapshots*are*related to special events that do not concern the whole population of Abidjan, but*are**localized*. ... Therefore, the snapshot*graph*is a*clique*, as all pairs of vertices share an edge. ...##
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Programming with personalized pagerank

2013
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Proceedings of the 22nd ACM international conference on Conference on information & knowledge management - CIKM '13
*

Here we present a firstorder probabilistic language which is well-suited to approximate "

doi:10.1145/2505515.2505573
dblp:conf/cikm/WangMC13
fatcat:o7zm4oqhurfrbbbmvkettykdsy
*local*" grounding: in particular, every query Q can be approximately grounded with a small*graph*. ... However, most probabilistic first-order logics*are*not efficient enough for realisticallysized instances of these tasks. ... Acknowledgements We*are*grateful to anonymous reviewers for useful comments. This work was sponsored in part by DARPA grant FA87501220342 to CMU and a Google Research Award. ...
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