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Locally C6 graphs are clique divergent

F. Larrión, V. Neumann-Lara
2000 Discrete Mathematics  
We prove that all 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.  ... 
doi:10.1016/s0012-365x(99)00233-2 fatcat:vvjpwiucjjfklf4rdbdrp7v7y4

Clique divergent graphs with unbounded sequence of diameters

F. Larrión, V. Neumann-Lara
1999 Discrete Mathematics  
The iterated 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.  ... 
doi:10.1016/s0012-365x(99)90105-x fatcat:cbfmrnr43napdhhm6vgcbovg6u

Unsupervised analysis of activity sequences using event-motifs

Raffay Hamid, Siddhartha Maddi, Aaron Bobick, Irfan Essa
2006 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 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.  ... 
doi:10.1145/1178782.1178794 fatcat:lynftlpb3zbifacww4a3njwbkm

A Transcriptome Community-and-Module Approach of the Human Mesoconnectome

Omar Paredes, Jhonatan B. López, César Covantes-Osuna, Vladimir Ocegueda-Hernández, Rebeca Romo-Vázquez, J. Alejandro Morales
2021 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.  ... 
doi:10.3390/e23081031 fatcat:yta4gheulbfnbl5pqf637myl7e

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

Shivani Bathla, Vinita Vasudevan
2022 arXiv   pre-print
Nodes 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 .  ... 
arXiv:2202.12003v1 fatcat:kl37t4gg2bd5tfy7dil6d3kcgq

Landmarks Augmentation with Manifold-Barycentric Oversampling [article]

Iaroslav Bespalov, Nazar Buzun, Oleg Kachan, Dmitry V. Dylov
2021 arXiv   pre-print
The proposed algorithm finds 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.  ... 
arXiv:2104.00925v2 fatcat:ucwztbpbnjhglpdszccw6gnxvm

Variational Approximations between Mean Field Theory and the Junction Tree Algorithm [article]

Wim Wiegerinck
2013 arXiv   pre-print
We also show how the method fits into some other variational approximations that 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.  ... 
arXiv:1301.3901v1 fatcat:hwcooxop7bgx3fobwznhkxczpe

Chromatic transitions in the emergence of syntax networks

Bernat Corominas-Murtra, Martí Sànchez Fibla, Sergi Valverde, Ricard Solé
2018 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 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] .  ... 
doi:10.1098/rsos.181286 pmid:30662738 pmcid:PMC6304139 fatcat:olpfdqej5nadlntn3kxlxpwz5u

Semantic Divergence Based Evaluation of Web Service Communities

Hafida Naim, Mustapha Aznag, Mohamed Quafafou, Nicolas Durand
2016 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 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.  ... 
doi:10.1109/scc.2016.101 dblp:conf/IEEEscc/NaimAQD16 fatcat:npufrbqrhzgu7ictbipuottunq

Preserving Minority Structures in Graph Sampling [article]

Ying Zhao, Haojin Jiang, Qi'an Chen, Yaqi Qin, Huixuan Xie, Yitao Wu Shixia Liu, Zhiguang Zhou, Jiazhi Xia, Fangfang Zhou
2020 arXiv   pre-print
By comprehensively analyzing the literature on 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  ... 
arXiv:2009.02498v2 fatcat:uzj6thjf2nbwnjqrgrewxs6zca

Exploring complex networks

Steven H. Strogatz
2001 Nature  
If Q < 0, the 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.  ... 
doi:10.1038/35065725 pmid:11258382 fatcat:wv7tm56dpjed3bvr2tyvs7yqnu

Specificity determinants and diversification of the Brassica self-incompatibility pollen ligand

T. Chookajorn, A. Kachroo, D. R. Ripoll, A. G. Clark, J. B. Nasrallah
2003 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 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.  ... 
doi:10.1073/pnas.2637116100 pmid:14694189 pmcid:PMC327116 fatcat:bm7i3va755burptule5dap7g74

The complexity of pure Nash equilibria

Alex Fabrikant, Christos Papadimitriou, Kunal Talwar
2004 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing - STOC '04  
We investigate from the computational viewpoint multi-player games that 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) .  ... 
doi:10.1145/1007352.1007445 dblp:conf/stoc/FabrikantPT04 fatcat:iolkx27lf5ebplvjx7igubyuau

Classifying call profiles in large-scale mobile traffic datasets

Diala Naboulsi, Razvan Stanica, Marco Fiore
2014 IEEE INFOCOM 2014 - IEEE Conference on Computer Communications  
Cellular communications 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.  ... 
doi:10.1109/infocom.2014.6848119 dblp:conf/infocom/NaboulsiSF14 fatcat:ctygxtdx2vcopjoudcpsi5maza

Programming with personalized pagerank

William Yang Wang, Kathryn Mazaitis, William W. Cohen
2013 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 "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.  ... 
doi:10.1145/2505515.2505573 dblp:conf/cikm/WangMC13 fatcat:o7zm4oqhurfrbbbmvkettykdsy
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