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Academic literature on the topic 'Small world graph'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Small world graph"

1

Cont, Rama, and Emily Tanimura. "Small-world graphs: characterization and alternative constructions." Advances in Applied Probability 40, no. 4 (December 2008): 939–65. http://dx.doi.org/10.1239/aap/1231340159.

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Small-world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small-world graphs, based on a probabilistic formulation of scaling properties of the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), which are based on random perturbations of a regular lattice. We also propose alternative constructions of small-world graphs which are not based on lattices and study their scaling properties.

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Cont, Rama, and Emily Tanimura. "Small-world graphs: characterization and alternative constructions." Advances in Applied Probability 40, no. 04 (December 2008): 939–65. http://dx.doi.org/10.1017/s0001867800002913.

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Small-world graphs are examples of random graphs which mimic empirically observed features of social networks. We propose an intrinsic definition of small-world graphs, based on a probabilistic formulation of scaling properties of the graph, which does not rely on any particular construction. Our definition is shown to encompass existing models of small-world graphs, proposed by Watts (1999) and studied by Barbour and Reinert (2001), which are based on random perturbations of a regular lattice. We also propose alternative constructions of small-world graphs which are not based on lattices and study their scaling properties.

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Wong, Pak Chung, Harlan Foote, Patrick Mackey, George Chin, Heidi Sofia, and Jim Thomas. "A Dynamic Multiscale Magnifying Tool for Exploring Large Sparse Graphs." Information Visualization 7, no. 2 (April 17, 2008): 105–17. http://dx.doi.org/10.1057/palgrave.ivs.9500177.

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We present an information visualization tool, known as GreenMax, to visually explore large small-world graphs with up to a million graph nodes on a desktop computer. A major motivation for scanning a small-world graph in such a dynamic fashion is the demanding goal of identifying not just the well-known features but also the unknown–known and unknown–unknown features of the graph. GreenMax uses a highly effective multilevel graph drawing approach to pre-process a large graph by generating a hierarchy of increasingly coarse layouts that later support the dynamic zooming of the graph. This paper describes the graph visualization challenges, elaborates our solution, and evaluates the contributions of GreenMax in the larger context of visual analytics on large small-world graphs. We report the results of two case studies using GreenMax and the results support our claim that we can use GreenMax to locate unexpected features or structures behind a graph.

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Bassett, Danielle S., and Edward T. Bullmore. "Small-World Brain Networks Revisited." Neuroscientist 23, no. 5 (September 21, 2016): 499–516. http://dx.doi.org/10.1177/1073858416667720.

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It is nearly 20 years since the concept of a small-world network was first quantitatively defined, by a combination of high clustering and short path length; and about 10 years since this metric of complex network topology began to be widely applied to analysis of neuroimaging and other neuroscience data as part of the rapid growth of the new field of connectomics. Here, we review briefly the foundational concepts of graph theoretical estimation and generation of small-world networks. We take stock of some of the key developments in the field in the past decade and we consider in some detail the implications of recent studies using high-resolution tract-tracing methods to map the anatomical networks of the macaque and the mouse. In doing so, we draw attention to the important methodological distinction between topological analysis of binary or unweighted graphs, which have provided a popular but simple approach to brain network analysis in the past, and the topology of weighted graphs, which retain more biologically relevant information and are more appropriate to the increasingly sophisticated data on brain connectivity emerging from contemporary tract-tracing and other imaging studies. We conclude by highlighting some possible future trends in the further development of weighted small-worldness as part of a deeper and broader understanding of the topology and the functional value of the strong and weak links between areas of mammalian cortex.

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Acharjee, Santanu, Bijit Bora, and Robin I. M. Dunbar. "On M-Polynomials of Dunbar Graphs in Social Networks." Symmetry 12, no. 6 (June 3, 2020): 932. http://dx.doi.org/10.3390/sym12060932.

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Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We develop a novel application of M-polynomials, the ( m , n , r ) -agent recruitment graph where n > 1 , to study the relationship between the Dunbar graphs of social networks and the small-world phenomenon. We show that the small-world effects are only possible if everyone uses the full range of their network when selecting steps in the small-world chain. Topological indices may provide valuable insights into the structure and dynamics of social network graphs because they incorporate an important element of the dynamical transitivity of such graphs.

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Roux, Jérôme, Nicolas Bez, Paul Rochet, Rocío Joo, and Stéphanie Mahévas. "Graphlet correlation distance to compare small graphs." PLOS ONE 18, no. 2 (February 15, 2023): e0281646. http://dx.doi.org/10.1371/journal.pone.0281646.

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Graph models are standard for representing mutual relationships between sets of entities. Often, graphs deal with a large number of entities with a small number of connections (e.g. social media relationships, infectious disease spread). The distances or similarities between such large graphs are known to be well established by the Graphlet Correlation Distance (GCD). This paper deals with small graphs (with potentially high densities of connections) that have been somewhat neglected in the literature but that concern important fora like sociology, ecology and fisheries, to mention some examples. First, based on numerical experiments, we study the conditions under which Erdős-Rényi, Fitness Scale-Free, Watts-Strogatz small-world and geometric graphs can be distinguished by a specific GCD measure based on 11 orbits, the GCD11. This is done with respect to the density and the order (i.e. the number of nodes) of the graphs when comparing graphs with the same and different orders. Second, we develop a randomization statistical test based on the GCD11 to compare empirical graphs to the four possible null models used in this analysis and apply it to a fishing case study where graphs represent pairwise proximity between fishing vessels. The statistical test rules out independent pairing within the fleet studied which is a standard assumption in fisheries. It also illustrates the difficulty to identify similarities between real-world small graphs and graph models.

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Liao, Yunhua, Yaoping Hou, and Xiaoling Shen. "Tutte polynomial of a small-world Farey graph." EPL (Europhysics Letters) 104, no. 3 (November 1, 2013): 38001. http://dx.doi.org/10.1209/0295-5075/104/38001.

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Li, Jonathan, Rohan Potru, and Farhad Shahrokhi. "A Performance Study of Some Approximation Algorithms for Computing a Small Dominating Set in a Graph." Algorithms 13, no. 12 (December 14, 2020): 339. http://dx.doi.org/10.3390/a13120339.

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We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the greedy and LP rounding algorithms. Over the range of test data, all algorithms perform better than anticipated in theory, and have small performance ratios, measured as the size of output divided by the LP objective lower bound. However, each have advantages over the others. For instance, LP rounding algorithm normally outperforms the other algorithms on sparse real-world graphs. On a graph with 400,000+ vertices, LP rounding took less than 15 s of CPU time to generate a solution with performance ratio 1.011, while the greedy and hybrid algorithms generated solutions of performance ratio 1.12 in similar time. For synthetic graphs, the hybrid algorithm normally outperforms the others, whereas for hypercubes and k-Queens graphs, greedy outperforms the rest. Another advantage of the hybrid algorithm is to solve very large problems that are suitable for application of LP rounding (sparse graphs) but LP formulations become formidable in practice and LP solvers crash, as we observed on a real-world graph with 7.7 million+ vertices and a planar graph on 1,000,000 vertices.

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Zhang, Lixia, and Jianliang Gao. "Incremental Graph Pattern Matching Algorithm for Big Graph Data." Scientific Programming 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/6749561.

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Graph pattern matching is widely used in big data applications. However, real-world graphs are usually huge and dynamic. A small change in the data graph or pattern graph could cause serious computing cost. Incremental graph matching algorithms can avoid recomputing on the whole graph and reduce the computing cost when the data graph or the pattern graph is updated. The existing incremental algorithm PGC_IncGPM can effectively reduce matching time when no more than half edges of the pattern graph are updated. However, as the number of changed edges increases, the improvement of PGC_IncGPM gradually decreases. To solve this problem, an improved algorithm iDeltaP_IncGPM is developed in this paper. For multiple insertions (resp., deletions) on pattern graphs, iDeltaP_IncGPM determines the nodes’ matching state detection sequence and processes them together. Experimental results show that iDeltaP_IncGPM has higher efficiency and wider application range than PGC_IncGPM.

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Ganesh, Ayalvadi, and Feng Xue. "On the connectivity and diameter of small-world networks." Advances in Applied Probability 39, no. 4 (December 2007): 853–63. http://dx.doi.org/10.1239/aap/1198177228.

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We consider two different models of small-world graphs on nodes whose locations are modelled by a stochastic point process. In the first model each node is connected to a fixed number of its nearest neighbours, while in the second model each node is connected to all nodes located within some fixed distance. In both models, nodes are additionally connected via shortcuts to other nodes chosen uniformly at random. We obtain sufficient conditions for connectivity in the first model, and necessary conditions in the second model. Thereby, we show that connectivity is achieved at a smaller value of total degree (nearest neighbours plus shortcuts) in the first model. We also obtain bounds on the diameter of the graph in this model.

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Dissertations / Theses on the topic "Small world graph"

1

Allen, Andrea J. "Average Shortest Path Length in a Novel Small-World Network." Oberlin College Honors Theses / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1516362622694547.

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Luo, Yongfeng. "Range-Based Graph Clustering." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1014606422.

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Damaj, Samer. "SWH, application "Small-world" à la génération des réseaux d'interconnexion pour les architectures massivement parallèles." Brest, 2011. http://www.theses.fr/2011BRES2076.

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Les possibilités d'intégration sont de plus en plus importantes et le nombre de transistors disponibles sur un composant n'est plus aussi critique que dans le passé. Cependant les structures de traitement du type monoprocesseur ne bénéficient plus de cette augmentation de ressources et on voit apparaître des composants du type MP Soc (multiprocessors on Chip) qui intègre plusieurs coeurs de processeur sur une même puce. Le problème consiste donc à faire passer à l'échelle des architectures systèmes du type MIMD (Multiple Instruction stream Multiple Data stream). Si on considère des coeurs de processeur complexe alors le problème reste actuellement assez maîtrisable car leur nombre reste limité (2 voit 4 processeurs). Par contre l'utilisation de noeuds de traitement de plus petite taille autorise l'intégration de dizaines voire de centaines de processeurs sur un même circuit. Les besoins en puissance de calcul ne se satisfont plus des limites rencontrées sur des processeurs complexes. La généralisation des composants du type MPSoC qui intègrent un nombre toujours plus important de processeurs sur une puce. Cependant, interconnecter un grand nombre de processeurs sur une puce est un délicat. Essentiellement, les structures adaptées aux contraintes de la puce sont trop peu générales, et les schémas de l’interconnexion plus globale engendrent des coûts de fabrication trop élevés. Ce problème se décompose en deux sous problèmes intimement liés qui sont la recherche d'une topologie permettant d'atteindre un niveau de connectivité acceptable et le coût matériel de sa réalisation. C'est dans ce dernier cas qui s'inscrit le contexte scientifique de ce mémoire. Les concepteurs se basent sur des différentes architectures pour réaliser des puces. Les architectures à mémoire partagée où il y a une saturation d’accès mémoire avec un grand nombre de PEs (Processeurs Élémentaires) comme par exemple TILERA Corporation. Les architectures à mémoire distribué où il se manifeste le problème des programmes fortement communicants. Ce type d'architecture est structuré autour d'un Noc (Network-on-Chip). De nombreuses études ont déjà été réalisées sur la problématique des architectures et de leurs réalisations avec pour motivations de trouver une manière élégante de supporter des Pes qui est de plus en plus nombreux et rapide en limitant le nombre de fils et pour obtenir des réseaux réguliers où le coût et le temps de développement du layout sont très court. Pour cette raison, nous sommes à la recherche d'une nouvelle plate-forme homogène avec des multicoeurs réguliers et massivement parallèles. C'est dans ce dernier cas qui s'inscrit le contexte industriel de ce mémoire de thèse. Pour des raisons techniques, il faut rendre les circuits homogènes, réguliers et denses parce que le coût et le temps de développement du layout d'un circuit non régulier sont très longs. Pour cette raison, il faut s'appuyer sur des architectures massivement parallèles. Les processeurs doivent communiquer entre eux, ils sont donc connectés via un réseau qui implémente une topologie. Pour une topologie donnée, on dispose de métriques grossières telles que le nombre de noeuds (le nombre de sommets dans un graphe donné), le degré (le nombre de liens entrants et sortants pour chaque sommet dans ce graphe donné) et le diamètre (la distance maximale entre deux noeuds ou sommets quelconques dans le graphe). Dans ce cas, comme on veut un circuit régulier, où les CPUs sont organisés en grille 2D pour les techniques actuels et éventuellement 3D pour les futurs techniques alors il faut obtenir le coût silicium pour mapper la topologie choisie sur cette grille. Le passage de la topologie (mapping) à la réalisation sera qualifié de placement-routage" physique (le terme "placement" veut dire de placer les sommets de ce graphe donné sur une grille 2D et le terme "routage" veut dire de faire communiquer ces sommets entre eux)
Graphs with a minimum diameter have applications in the design of building-block switching systems, communication networks, and distributed computer systems. Several methods of constructing directed graphs with a small diameter are proposed. First, the dissertation presents as background several (delta, D) graphs including the Hypercube and de Bruijn. It shows the major disadvantages when implementing these topologies in practice for large scale. To achieve our goal, we propose a regular graph called Small World Heuristic (SWH) suitable for large parallel computers. This graph has a maximum degree ! and a small diameter D, while maintaining an acceptable level of connectivity. We show that this heuristic can connect on short distance thousands of nodes as little as 4 links per node. ̕Finally, we present a new integrated placement and routing algorithm to implement this heuristic on 2D VLSI

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ZHONG, LI. "SHORTCUT BASED GRAPH COARSENING FOR PROTEIN INTERACTION NETWORK VISUALIZATION." University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin997457452.

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Balakrishnan, Hemant. "ALGORITHMS FOR DISCOVERING COMMUNITIES IN COMPLEX NETWORKS." Doctoral diss., University of Central Florida, 2006. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2478.

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It has been observed that real-world random networks like the WWW, Internet, social networks, citation networks, etc., organize themselves into closely-knit groups that are locally dense and globally sparse. These closely-knit groups are termed communities. Nodes within a community are similar in some aspect. For example in a WWW network, communities might consist of web pages that share similar contents. Mining these communities facilitates better understanding of their evolution and topology, and is of great theoretical and commercial significance. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network, whereas community identification is the problem of identifying the community, to which, a given set of nodes belong. We make a comparative study of various existing community-discovery algorithms. We then propose a new algorithm based on bibliographic metrics, which addresses the drawbacks in existing approaches. Bibliographic metrics are used to study similarities between publications in a citation network. Our algorithm classifies nodes in the network based on the similarity of their neighborhoods. One of the drawbacks of the current community-discovery algorithms is their computational complexity. These algorithms do not scale up to the enormous size of the real-world networks. We propose a hash-table-based technique that helps us compute the bibliometric similarity between nodes in O(m ?) time. Here m is the number of edges in the graph and ?, the largest degree. Next, we investigate different centrality metrics. Centrality metrics are used to portray the importance of a node in the network. We propose an algorithm that utilizes centrality metrics of the nodes to compute the importance of the edges in the network. Removal of the edges in ascending order of their importance breaks the network into components, each of which represent a community. We compare the performance of the algorithm on synthetic networks with a known community structure using several centrality metrics. Performance was measured as the percentage of nodes that were correctly classified. As an illustration, we model the ucf.edu domain as a web graph and analyze the changes in its properties like densification power law, edge density, degree distribution, diameter, etc., over a five-year period. Our results show super-linear growth in the number of edges with time. We observe (and explain) that despite the increase in average degree of the nodes, the edge density decreases with time.
Ph.D.
School of Electrical Engineering and Computer Science
Engineering and Computer Science
Computer Science

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BORRELLO, DAVIDE. "Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2009. http://hdl.handle.net/10281/7467.

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The main subject of the thesis is concerned with interacting particle systems, which are classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other. The particles move on a finite or infinite discrete space and on each element of this space the state of the configuration is integer valued. Configurations of particles evolve in continuous time according to a Markov process. Here the space is either the infinite deterministic d-dimensional lattice or a random graph given by the finite d-dimensional torus with random matchings. In Part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice: stochastic order is a key tool to understand the ergodic properties of a system. We give applications on biological models of spread of epidemics and metapopulation dynamics systems. In Part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs. We derive the law of the meeting time of two random walks on small world graphs and we use this result to understand the role of random connections in meeting time of random walks and to investigate the behavior of coalescing random walks.

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Holme, Petter. "Form and function of complex networks." Doctoral thesis, Umeå : Univ, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-222.

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Duarte, Gerdivane Ferreira. "F?sica estat?stica aplicada a sistemas sociais atrav?s do estudo de redes complexas." Universidade Federal do Rio Grande do Norte, 2014. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18609.

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Made available in DSpace on 2015-03-03T15:15:30Z (GMT). No. of bitstreams: 1 GerdivaneFD_DISSERT.pdf: 2461999 bytes, checksum: afd653d46e87e83d8b0144e8086a3d19 (MD5) Previous issue date: 2014-02-21
Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior
In this work a study of social networks based on analysis of family names is presented. A basic approach to the mathematical formalism of graphs is developed and then main theoretical models for complex networks are presented aiming to support the analysis of surnames networks models. These, in turn, are worked so as to be drawn leading quantities, such as aggregation coefficient, minimum average path length and connectivity distribution. Based on these quantities, it can be stated that surnames networks are an example of complex network, showing important features such as preferential attachment and small-world character
Neste trabalho ? apresentado um estudo das redes sociais baseado na an?lise dos nomes de fam?lias. Faz-se uma abordagem b?sica do formalismo matem?tico dos grafos e em seguida apresenta-se os principais modelos te?ricos para as Redes Complexas com o objetivo de fundamentar a an?lise das redes dos sobrenomes. Estas, por sua vez, s?o trabalhadas de modo a serem extra?das as principais grandezas, tais como coe ciente de agrega??o, menor caminho m?dio e distribui??o de conectividades. Com base nestas grandezas, pode-se a rmar que as redes de sobrenomes s?o um exemplo de rede complexa, exibindo caracter?sticas importantes como liga??o preferencial e o car?ter de mundo pequeno.

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Zhuang, Yuwen. "Metric Based Automatic Event Segmentation and Network Properties Of Experience Graphs." The Ohio State University, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=osu1337372416.

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Montilla, Michaela. "Vliv parcelačního atlasu na kvalitu klasifikace pacientů s neurodegenerativním onemocněním." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2018. http://www.nusl.cz/ntk/nusl-378150.

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The aim of the thesis is to define the dependency of the classification of patients affected by neurodegenerative diseases on the choice of the parcellation atlas. Part of this thesis is the application of the functional connectivity analysis and the calculation of graph metrics according to the method published by Olaf Sporns and Mikail Rubinov [1] on fMRI data measured at CEITEC MU. The application is preceded by the theoretical research of parcellation atlases for brain segmentation from fMRI frames and the research of mathematical methods for classification as well as classifiers of neurodegenerative diseases. The first chapters of the thesis brings a theoretical basis of knowledge from the field of magnetic and functional magnetic resonance imaging. The physical principles of the method, the conditions and the course of acquisition of image data are defined. The third chapter summarizes the graph metrics used in the diploma thesis for analyzing and classifying graphs. The paper presents a brief overview of the brain segmentation methods, with the focuse on the atlas-based segmentation. After a theoretical research of functional connectivity methods and mathematical classification methods, the findings were used for segmentation, calculation of graph metrics and for classification of fMRI images obtained from 96 subjects into the one of two classes using Binary classifications by support vector machines and linear discriminatory analysis. The data classified in this study was measured on patiens with Parkinson’s disease (PD), Alzheimer’s disease (AD), Mild cognitive impairment (MCI), a combination of PD and MCI and subjects belonging to the control group of healthy individuals. For pre-processing and analysis, the MATLAB environment, the SPM12 toolbox and The Brain Connectivity Toolbox were used.

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Books on the topic "Small world graph"

1

Large networks and graph limits. Providence, Rhode Island: American Mathematical Society, 2012.

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Bader, David A., 1969- editor of compilation, Meyerhenke, Henning, 1978- editor of compilation, Sanders, Peter, editor of compilation, and Wagner, Dorothea, 1957- editor of compilation, eds. Graph partitioning and graph clustering: 10th DIMACS Implementation Challenge Workshop, February 13-14, 2012, Georgia Institute of Technology, Atlanta, GA. Providence, Rhode Island: American Mathematical Society, 2013.

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Watts, Duncan J. Small worlds: The dynamics of networks between order and randomness. Princeton, N.J: Princeton University Press, 1999.

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Patterns, Dancing Dolphin. Imagine a World Where Fabric Is Free & Cross Stitch Makes You Thin: Assortment of Large and Small Graph Paper for Planning Designs. Independently published, 2019.

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Garza, Berniea. Be a Fruit Loop in a World of Cheerios Motivation Journal /Notebook with Motivation and Inspirational Quote for Motivation Quotes Lovers: Journal Dot-Grid,Graph,Lined,Blank No Lined, Small Pocket Notebook Journal Diary, 120 Pages. Independently Published, 2020.

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Garza, Berniea. Everyone Thinks of Changing the World, but No One Thinks of Changing Himself Motivation Journal /Notebook with Motivation and Inspirational Quote for Motivation: Journal Dot-Grid,Graph,Lined,Blank No Lined, Small Pocket Notebook Journal Diary, 120 Pages. Independently Published, 2020.

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Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton, 1999.

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Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton, New Jersey: Princeton University Press, 1999.

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Vernizzi, Graziano, and Henri Orland. Complex networks. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.43.

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This article deals with complex networks, and in particular small world and scale free networks. Various networks exhibit the small world phenomenon, including social networks and gene expression networks. The local ordering property of small world networks is typically associated with regular networks such as a 2D square lattice. The small world phenomenon can be observed in most scale free networks, but few small world networks are scale free. The article first provides a brief background on small world networks and two models of scale free graphs before describing the replica method and how it can be applied to calculate the spectral densities of the adjacency matrix and Laplacian matrix of a scale free network. It then shows how the effective medium approximation can be used to treat networks with finite mean degree and concludes with a discussion of the local properties of random matrices associated with complex networks.

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Small Worlds: The Dynamics of Networks between Order and Randomness (Princeton Studies in Complexity). Princeton University Press, 2003.

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Book chapters on the topic "Small world graph"

1

Gros, Claudius. "Graph Theory and Small-World Networks." In Complex and Adaptive Dynamical Systems, 1–38. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-04706-0_1.

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Gros, Claudius. "Graph Theory and Small-World Networks." In Complex and Adaptive Dynamical Systems, 1–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-71874-1_1.

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Gros, Claudius. "Graph Theory and Small-World Networks." In Complex and Adaptive Dynamical Systems, 1–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36586-7_1.

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Gros, Claudius. "Graph Theory and Small-World Networks." In Complex and Adaptive Dynamical Systems, 1–42. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16265-2_1.

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Zhao, Chenggui. "Circulant Graph Modeling Deterministic Small-World Networks." In Communications in Computer and Information Science, 124–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-18134-4_20.

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Duchon, Philippe, Nicolas Hanusse, Emmanuelle Lebhar, and Nicolas Schabanel. "Could any Graph be Turned into a Small-World?" In Lecture Notes in Computer Science, 511–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11561927_46.

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Heydenreich, Markus, and Christian Hirsch. "A Spatial Small-World Graph Arising from Activity-Based Reinforcement." In Lecture Notes in Computer Science, 102–14. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-25070-6_8.

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Ille, Sebastian. "Social Networks and Graph Theory: Small World Effects and Social Change." In Models of Society and Complex Systems, 117–45. London: Routledge, 2022. http://dx.doi.org/10.4324/9781003035329-6.

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Andersen, Reid, Fan Chung, and Lincoln Lu. "Analyzing the Small World Phenomenon Using a Hybrid Model with Local Network Flow (Extended Abstract)." In Algorithms and Models for the Web-Graph, 19–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-30216-2_2.

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Brandes, Ulrik, Daniel Fleischer, and Thomas Puppe. "Dynamic Spectral Layout of Small Worlds." In Graph Drawing, 25–36. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11618058_3.

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Conference papers on the topic "Small world graph"

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Gibson, Helen, and Joe Faith. "Node-attribute Graph Layout for Small-World Networks." In 2011 15th International Conference Information Visualisation (IV). IEEE, 2011. http://dx.doi.org/10.1109/iv.2011.64.

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Nguyen, Van, and Chip Martel. "Augmented Graph Models for Small-World Analysis with Geographical Factors." In 2008 Proceedings of the Fifth Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2008. http://dx.doi.org/10.1137/1.9781611972986.5.

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Daraghmi, Eman Yasser, and Yuan Shyan Ming. "Using graph theory to re-verify the small world theory in an online social network word." In the 14th International Conference. New York, New York, USA: ACM Press, 2012. http://dx.doi.org/10.1145/2428736.2428811.

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Zhang, Zhen, Wenjun Xiao, and Xiaoming Wang. "General Method to Build Deterministic Small-World Networks Based on Cayley Graph." In 2009 Second International Workshop on Computer Science and Engineering. IEEE, 2009. http://dx.doi.org/10.1109/wcse.2009.717.

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Dong, Andy. "Design Innovation Through Transformation." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-46032.

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The act of changing a product by substituting technologies remains a challenging problem for companies with incumbent and dominant designs. This paper describes a new method to quantify the degree of this change based on the graph edit distance of functional models of products. The knowledge structure of a product is represented by its functional model using the ontology of the functional basis. Its knowledge structure is then compared to an equivalent small-world graph, widely regarded as the most efficient structure for information sharing. Finally, the graph edit distance between a product model and its equivalent small-world graph is calculated. This paper demonstrates a general purpose manner to study design innovation through technological transformation.

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Bader, David A., and Kamesh Madduri. "SNAP, Small-world Network Analysis and Partitioning: An open-source parallel graph framework for the exploration of large-scale networks." In Distributed Processing Symposium (IPDPS). IEEE, 2008. http://dx.doi.org/10.1109/ipdps.2008.4536261.

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Yu, Jing, Yuan Chai, Yujing Wang, Yue Hu, and Qi Wu. "CogTree: Cognition Tree Loss for Unbiased Scene Graph Generation." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/176.

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Scene graphs are semantic abstraction of images that encourage visual understanding and reasoning. However, the performance of Scene Graph Generation (SGG) is unsatisfactory when faced with biased data in real-world scenarios. Conventional debiasing research mainly studies from the view of balancing data distribution or learning unbiased models and representations, ignoring the correlations among the biased classes. In this work, we analyze this problem from a novel cognition perspective: automatically building a hierarchical cognitive structure from the biased predictions and navigating that hierarchy to locate the relationships, making the tail relationships receive more attention in a coarse-to-fine mode. To this end, we propose a novel debiasing Cognition Tree (CogTree) loss for unbiased SGG. We first build a cognitive structure CogTree to organize the relationships based on the prediction of a biased SGG model. The CogTree distinguishes remarkably different relationships at first and then focuses on a small portion of easily confused ones. Then, we propose a debiasing loss specially for this cognitive structure, which supports coarse-to-fine distinction for the correct relationships. The loss is model-agnostic and consistently boosting the performance of several state-of-the-art models. The code is available at: https://github.com/CYVincent/Scene-Graph-Transformer-CogTree.

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Out, Charlotte, and Ahad N. Zehmakan. "Majority Vote in Social Networks: Make Random Friends or Be Stubborn to Overpower Elites." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/49.

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Consider a graph G, representing a social network. Assume that initially each node is colored either black or white, which corresponds to a positive or negative opinion regarding a consumer product or a technological innovation. In the majority model, in each round all nodes simultaneously update their color to the most frequent color among their connections. Experiments on the graph data from the real world social networks (SNs) suggest that if all nodes in an extremely small set of high-degree nodes, often referred to as the elites, agree on a color, that color becomes the dominant color at the end of the process. We propose two countermeasures that can be adopted by individual nodes relatively easily and guarantee that the elites will not have this disproportionate power to engineer the dominant output color. The first countermeasure essentially requires each node to make some new connections at random while the second one demands the nodes to be more reluctant towards changing their color (opinion). We verify their effectiveness and correctness both theoretically and experimentally. We also investigate the majority model and a variant of it when the initial coloring is random on the real world SNs and several random graph models. In particular, our results on the Erdős-Rényi, and regular random graphs confirm or support several theoretical findings or conjectures by the prior work regarding the threshold behavior of the process. Finally, we provide theoretical and experimental evidence for the existence of a poly-logarithmic bound on the expected stabilization time of the majority model.

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Yang, Shuo, Zhiqiang Zhang, Jun Zhou, Yang Wang, Wang Sun, Xingyu Zhong, Yanming Fang, Quan Yu, and Yuan Qi. "Financial Risk Analysis for SMEs with Graph-based Supply Chain Mining." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/643.

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Small and Medium-sized Enterprises (SMEs) are playing a vital role in the modern economy. Recent years, financial risk analysis for SMEs attracts lots of attentions from financial institutions. However, the financial risk analysis for SMEs usually suffers data deficiency problem, especially for the mobile financial institutions which seldom collect credit-related data directly from SMEs. Fortunately, although credit-related information of SMEs is hard to be acquired sufficiently, the interactive relationships between SMEs, which may contain valuable information of financial risk, is usually available for the mobile financial institutions. Finding out credit-related relationship of SME from massive interactions helps comprehensively model the SMEs thus improve the performance of financial risk analysis. In this paper, tackling the data deficiency problem of financial risk analysis for SMEs, we propose an innovative financial risk analysis framework with graph-based supply chain mining. Specifically, to capture the credit-related topology structural and temporal variation information of SMEs, we design and employ a novel spatial-temporal aware graph neural network, to mine supply chain relationship on a SME graph, and then analysis the credit risk based on the mined supply chain graph. Experimental results on real-world financial datasets prove the effectiveness of our proposal for financial risk analysis for SMEs.

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Tran, Hung-Nghiep, and Atsuhiro Takasu. "MEIM: Multi-partition Embedding Interaction Beyond Block Term Format for Efficient and Expressive Link Prediction." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/314.

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Knowledge graph embedding aims to predict the missing relations between entities in knowledge graphs. Tensor-decomposition-based models, such as ComplEx, provide a good trade-off between efficiency and expressiveness, that is crucial because of the large size of real world knowledge graphs. The recent multi-partition embedding interaction (MEI) model subsumes these models by using the block term tensor format and provides a systematic solution for the trade-off. However, MEI has several drawbacks, some of which carried from its subsumed tensor-decomposition-based models. In this paper, we address these drawbacks and introduce the Multi-partition Embedding Interaction iMproved beyond block term format (MEIM) model, with independent core tensor for ensemble effects and soft orthogonality for max-rank mapping, in addition to multi-partition embedding. MEIM improves expressiveness while still being highly efficient, helping it to outperform strong baselines and achieve state-of-the-art results on difficult link prediction benchmarks using fairly small embedding sizes. The source code is released at https://github.com/tranhungnghiep/MEIM.

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Reports on the topic "Small world graph"

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Schulz, Jan, Daniel Mayerhoffer, and Anna Gebhard. A Network-Based Explanation of Perceived Inequality. Otto-Friedrich-Universität, 2021. http://dx.doi.org/10.20378/irb-49393.

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Across income groups and countries, the public perception of economic inequality and many other macroeconomic variables such as inflation or unemployment rates is spectacularly wrong. These misperceptions have far-reaching consequences, as it is perceived inequality, not actual inequality informing redistributive preferences. The prevalence of this phenomenon is independent of social class and welfare regime, which suggests the existence of a common mechanism behind public perceptions. We propose a network-based explanation of perceived inequality building on recent advances in random geometric graph theory. The literature has identified several stylised facts on how individual perceptions respond to actual inequality and how these biases vary systematically along the income distribution. Our generating mechanism can replicate all of them simultaneously. It also produces social networks that exhibit salient features of real-world networks; namely, they cannot be statistically distinguished from small-world networks, testifying to the robustness of our approach. Our results, therefore, suggest that homophilic segregation is a promising candidate to explain inequality perceptions with strong implications for theories of consumption behaviour.

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Morin, Shai, Gregory Walker, Linda Walling, and Asaph Aharoni. Identifying Arabidopsis thaliana Defense Genes to Phloem-feeding Insects. United States Department of Agriculture, February 2013. http://dx.doi.org/10.32747/2013.7699836.bard.

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The whitefly (Bemisia tabaci) is a serious agricultural pest that afflicts a wide variety of ornamental and vegetable crop species. To enable survival on a great diversity of host plants, whiteflies must have the ability to avoid or detoxify numerous different plant defensive chemicals. Such toxins include a group of insect-deterrent molecules called glucosinolates (GSs), which also provide the pungent taste of Brassica vegetables such as radish and cabbage. In our BARD grant, we used the whitefly B. tabaci and Arabidopsis (a Brassica plant model) defense mutants and transgenic lines, to gain comprehensive understanding both on plant defense pathways against whiteflies and whitefly defense strategies against plants. Our major focus was on GSs. We produced transgenic Arabidopsis plants accumulating high levels of GSs. At the first step, we examined how exposure to high levels of GSs affects decision making and performance of whiteflies when provided plants with normal levels or high levels of GSs. Our major conclusions can be divided into three: (I) exposure to plants accumulating high levels of GSs, negatively affected the performance of both whitefly adult females and immature; (II) whitefly adult females are likely to be capable of sensing different levels of GSs in their host plants and are able to choose, for oviposition, the host plant on which their offspring survive and develop better (preference-performance relationship); (III) the dual presence of plants with normal levels and high levels of GSs, confused whitefly adult females, and led to difficulties in making a choice between the different host plants. These findings have an applicative perspective. Whiteflies are known as a serious pest of Brassica cropping systems. If the differences found here on adjacent small plants translate to field situations, intercropping with closely-related Brassica cultivars could negatively influence whitefly population build-up. At the second step, we characterized the defensive mechanisms whiteflies use to detoxify GSs and other plant toxins. We identified five detoxification genes, which can be considered as putative "key" general induced detoxifiers because their expression-levels responded to several unrelated plant toxic compounds. This knowledge is currently used (using new funding) to develop a new technology that will allow the production of pestresistant crops capable of protecting themselves from whiteflies by silencing insect detoxification genes without which successful host utilization can not occur. Finally, we made an effort to identify defense genes that deter whitefly performance, by infesting with whiteflies, wild-type and defense mutated Arabidopsis plants. The infested plants were used to construct deep-sequencing expression libraries. The 30- 50 million sequence reads per library, provide an unbiased and quantitative assessment of gene expression and contain sequences from both Arabidopsis and whiteflies. Therefore, the libraries give us sequence data that can be mined for both the plant and insect gene expression responses. An intensive analysis of these datasets is underway. We also conducted electrical penetration graph (EPG) recordings of whiteflies feeding on Arabidopsis wild-type and defense mutant plants in order to determine the time-point and feeding behavior in which plant-defense genes are expressed. We are in the process of analyzing the recordings and calculating 125 feeding behavior parameters for each whitefly. From the analyses conducted so far we conclude that the Arabidopsis defense mutants do not affect adult feeding behavior in the same manner that they affect immatures development. Analysis of the immatures feeding behavior is not yet completed, but if it shows the same disconnect between feeding behavior data and developmental rate data, we would conclude that the differences in the defense mutants are due to a qualitative effect based on the chemical constituency of the phloem sap.

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