On Community Detection in Real-World Networks and the Importance of Degree Assortativity
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Analysis of Topological Characteristics of Huge Online Social Networking Services Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Young-Ho Eom, Sue Moon, Hawoong Jeong
1 Analysis of Topological Characteristics of Huge Online Social Networking Services Yong-Yeol Ahn, Seungyeop Han, Haewoon Kwak, Young-Ho Eom, Sue Moon, Hawoong Jeong Abstract— Social networking services are a fast-growing busi- the statistics severely and it is imperative to use large data sets ness in the Internet. However, it is unknown if online relationships in network structure analysis. and their growth patterns are the same as in real-life social It is only very recently that we have seen research results networks. In this paper, we compare the structures of three online social networking services: Cyworld, MySpace, and orkut, from large networks. Novel network structures from human each with more than 10 million users, respectively. We have societies and communication systems have been unveiled; just access to complete data of Cyworld’s ilchon (friend) relationships to name a few are the Internet and WWW [3] and the patents, and analyze its degree distribution, clustering property, degree Autonomous Systems (AS), and affiliation networks [4]. Even correlation, and evolution over time. We also use Cyworld data in the short history of the Internet, SNSs are a fairly new to evaluate the validity of snowball sampling method, which we use to crawl and obtain partial network topologies of MySpace phenomenon and their network structures are not yet studied and orkut. Cyworld, the oldest of the three, demonstrates a carefully. The social networks of SNSs are believed to reflect changing scaling behavior over time in degree distribution. The the real-life social relationships of people more accurately than latest Cyworld data’s degree distribution exhibits a multi-scaling any other online networks. -
Correlation in Complex Networks
Correlation in Complex Networks by George Tsering Cantwell A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the University of Michigan 2020 Doctoral Committee: Professor Mark Newman, Chair Professor Charles Doering Assistant Professor Jordan Horowitz Assistant Professor Abigail Jacobs Associate Professor Xiaoming Mao George Tsering Cantwell [email protected] ORCID iD: 0000-0002-4205-3691 © George Tsering Cantwell 2020 ACKNOWLEDGMENTS First, I must thank Mark Newman for his support and mentor- ship throughout my time at the University of Michigan. Further thanks are due to all of the people who have worked with me on projects related to this thesis. In alphabetical order they are Eliz- abeth Bruch, Alec Kirkley, Yanchen Liu, Benjamin Maier, Gesine Reinert, Maria Riolo, Alice Schwarze, Carlos Serván, Jordan Sny- der, Guillaume St-Onge, and Jean-Gabriel Young. ii TABLE OF CONTENTS Acknowledgments .................................. ii List of Figures ..................................... v List of Tables ..................................... vi List of Appendices .................................. vii Abstract ........................................ viii Chapter 1 Introduction .................................... 1 1.1 Why study networks?...........................2 1.1.1 Example: Modeling the spread of disease...........3 1.2 Measures and metrics...........................8 1.3 Models of networks............................ 11 1.4 Inference................................. -
Learning on Hypergraphs: Spectral Theory and Clustering
Learning on Hypergraphs: Spectral Theory and Clustering Pan Li, Olgica Milenkovic Coordinated Science Laboratory University of Illinois at Urbana-Champaign March 12, 2019 Learning on Graphs Graphs are indispensable mathematical data models capturing pairwise interactions: k-nn network social network publication network Important learning on graphs problems: clustering (community detection), semi-supervised/active learning, representation learning (graph embedding) etc. Beyond Pairwise Relations A graph models pairwise relations. Recent work has shown that high-order relations can be significantly more informative: Examples include: Understanding the organization of networks (Benson, Gleich and Leskovec'16) Determining the topological connectivity between data points (Zhou, Huang, Sch}olkopf'07). Graphs with high-order relations can be modeled as hypergraphs (formally defined later). Meta-graphs, meta-paths in heterogeneous information networks. Algorithmic methods for analyzing high-order relations and learning problems are still under development. Beyond Pairwise Relations Functional units in social and biological networks. High-order network motifs: Motif (Benson’16) Microfauna Pelagic fishes Crabs & Benthic fishes Macroinvertebrates Algorithmic methods for analyzing high-order relations and learning problems are still under development. Beyond Pairwise Relations Functional units in social and biological networks. Meta-graphs, meta-paths in heterogeneous information networks. (Zhou, Yu, Han'11) Beyond Pairwise Relations Functional units in social and biological networks. Meta-graphs, meta-paths in heterogeneous information networks. Algorithmic methods for analyzing high-order relations and learning problems are still under development. Review of Graph Clustering: Notation and Terminology Graph Clustering Task: Cluster the vertices that are \densely" connected by edges. Graph Partitioning and Conductance A (weighted) graph G = (V ; E; w): for e 2 E, we is the weight. -
Multiplex Conductance and Gossip Based Information Spreading in Multiplex Networks
1 Multiplex Conductance and Gossip Based Information Spreading in Multiplex Networks Yufan Huang, Student Member, IEEE, and Huaiyu Dai, Fellow, IEEE Abstract—In this network era, not only people are connected, different networks are also coupled through various interconnections. This kind of network of networks, or multilayer networks, has attracted research interest recently, and many beneficial features have been discovered. However, quantitative study of information spreading in such networks is essentially lacking. Despite some existing results in single networks, the layer heterogeneity and complicated interconnections among the layers make the study of information spreading in this type of networks challenging. In this work, we study the information spreading time in multiplex networks, adopting the gossip (random-walk) based information spreading model. A new metric called multiplex conductance is defined based on the multiplex network structure and used to quantify the information spreading time in a general multiplex network in the idealized setting. Multiplex conductance is then evaluated for some interesting multiplex networks to facilitate understanding in this new area. Finally, the tradeoff between the information spreading efficiency improvement and the layer cost is examined to explain the user’s social behavior and motivate effective multiplex network designs. Index Terms—Information spreading, multiplex networks, gossip algorithm, multiplex conductance F 1 INTRODUCTION N the election year, one of the most important tasks Arguably, this somewhat simplified version of multilayer I for presidential candidates is to disseminate their words networks already captures many interesting multi-scale and and opinions to voters in a fast and efficient manner. multi-component features, and serves as a good starting The underlying research problem on information spreading point for our intended study. -
Happiness Is Assortative in Online Social Networks
Happiness Is Assortative in Johan Bollen*,** Online Social Networks Indiana University Bruno Goncalves**̧ Indiana University Guangchen Ruan** Indiana University Abstract Online social networking communities may exhibit highly Huina Mao** complex and adaptive collective behaviors. Since emotions play such Indiana University an important role in human decision making, how online networks Downloaded from http://direct.mit.edu/artl/article-pdf/17/3/237/1662787/artl_a_00034.pdf by guest on 25 September 2021 modulate human collective mood states has become a matter of considerable interest. In spite of the increasing societal importance of online social networks, it is unknown whether assortative mixing of psychological states takes place in situations where social ties are mediated solely by online networking services in the absence Keywords of physical contact. Here, we show that the general happiness, Social networks, mood, sentiment, or subjective well-being (SWB), of Twitter users, as measured from a assortativity, homophily 6-month record of their individual tweets, is indeed assortative across the Twitter social network. Our results imply that online social A version of this paper with color figures is networks may be equally subject to the social mechanisms that cause available online at http://dx.doi.org/10.1162/ assortative mixing in real social networks and that such assortative artl_a_00034. Subscription required. mixing takes place at the level of SWB. Given the increasing prevalence of online social networks, their propensity to connect users with similar levels of SWB may be an important factor in how positive and negative sentiments are maintained and spread through human society. Future research may focus on how event-specific mood states can propagate and influence user behavior in “real life.” 1 Introduction Bird flocking and fish schooling are typical and well-studied examples of how large communities of relatively simple individuals can exhibit highly complex and adaptive behaviors at the collective level. -
Rumour Spreading and Graph Conductance∗
Rumour spreading and graph conductance∗ Flavio Chierichetti, Silvio Lattanzi, Alessandro Panconesi fchierichetti,lattanzi,[email protected] Dipartimento di Informatica Sapienza Universit`adi Roma October 12, 2009 Abstract if its completion time is poly-logarithmic in the size of We show that if a connected graph with n nodes has the network regardless of the source, and that it is slow conductance φ then rumour spreading, also known as otherwise. randomized broadcast, successfully broadcasts a mes- Randomized broadcast has been intensely investi- sage within O(log4 n/φ6) many steps, with high proba- gated (see the related-work section). Our long term bility, using the PUSH-PULL strategy. An interesting goal is to characterize a set of necessary and/or suffi- feature of our approach is that it draws a connection be- cient conditions for rumour spreading to be fast in a tween rumour spreading and the spectral sparsification given network. In this work, we provide a very general procedure of Spielman and Teng [23]. sufficient condition{ high conductance. Our main moti- vation comes from the study of social networks. Loosely 1 Introduction stated, we are looking after a theorem of the form \Ru- mour spreading is fast in social networks". Our result is Rumour spreading, also known as randomized broadcast a good step in this direction because there are reasons or randomized gossip (all terms that will be used as to believe that social networks have high conductance. synonyms throughout the paper), refers to the following This is certainly the case for preferential attachment distributed algorithm. Starting with one source node models such as that of [18]. -
Absorbing State 34, 36 Adaptive Boolean Networks 78 Adaptive Chemical Network 73 Adaptive Coupled Map Lattices 66 Adaptive Epide
239 Index a b absorbing state 34, 36 b-value 107, 109, 112, 119 adaptive Boolean networks 78 Bak–Sneppen model 74, 75 adaptive chemical network 73 benchmark 216, 217, 234 adaptive coupled map lattices 66 Bethe–Peierls approach 225 adaptive epidemiological network betweenness of a node 68 95 bill-tracking website 6 adaptive network of coupled biodiversity 46 oscillators 83 biological evolution 73 adaptive networks 63–66, 70–72, bipartite networks 211 74, 83, 90, 98, 100, 102 bipartite structure 216 adaptive rewiring 91, 92 bipartition 218, 220 adaptive SIS model 96 bipartitioning problem 219 adjacency matrix 9, 66, 206, 207, birth-death processes 31, 37 209–211, 217, 223 bisection problem 232 aftershock 108, 113, 121, bistability 27 125–129, 131, 134, 135, 137 bivariate analysis 164 aftershock magnitudes 127 bivariate measures 162 aftershock sequence 121, 123 bivariate nonlinear approaches aftershock sequences 136 163 agent-based models 73 bivariate time-series analysis agent-based simulation 172, 173, 178 frameworks 3 block-structure 201, 203, 217, air transportation network 2, 10 222, 234, 235 anti-epileptic drugs 159, 163 Boolean networks 65, 76, 79 assortative 67 bounded rationality 25 attractor 164 box-counting technique 112, 113 autoregressive modeling 161, brain 161 172, 175 Brownian motion 6, 7 avalanche size 139 burst-firing 169, 170 average shortest path length 167 bursting 166, 167, 170 Reviews of Nonlinear Dynamics and Complexity. Edited by Heinz Georg Schuster Copyright c 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: -
Dynamics of Dyads in Social Networks: Assortative, Relational, and Proximity Mechanisms
SO36CH05-Uzzi ARI 2 June 2010 23:8 Dynamics of Dyads in Social Networks: Assortative, Relational, and Proximity Mechanisms Mark T. Rivera,1 Sara B. Soderstrom,1 and Brian Uzzi1,2 1Department of Management and Organizations, Kellogg School of Management, Northwestern University, Evanston, Illinois 60208; email: [email protected], [email protected], [email protected] 2Northwestern University Institute on Complex Systems and Network Science (NICO), Evanston, Illinois 60208-4057 Annu. Rev. Sociol. 2010. 36:91–115 Key Words First published online as a Review in Advance on Annu. Rev. Sociol. 2010.36:91-115. Downloaded from arjournals.annualreviews.org embeddedness, homophily, complexity, organizations, network April 12, 2010 evolution by NORTHWESTERN UNIVERSITY - Evanston Campus on 07/13/10. For personal use only. The Annual Review of Sociology is online at soc.annualreviews.org Abstract This article’s doi: Embeddedness in social networks is increasingly seen as a root cause of 10.1146/annurev.soc.34.040507.134743 human achievement, social stratification, and actor behavior. In this arti- Copyright c 2010 by Annual Reviews. cle, we review sociological research that examines the processes through All rights reserved which dyadic ties form, persist, and dissolve. Three sociological mech- 0360-0572/10/0811-0091$20.00 anisms are overviewed: assortative mechanisms that draw attention to the role of actors’ attributes, relational mechanisms that emphasize the influence of existing relationships and network positions, and proximity mechanisms that focus on the social organization of interaction. 91 SO36CH05-Uzzi ARI 2 June 2010 23:8 INTRODUCTION This review examines journal articles that explain how social networks evolve over time. -
Random Boolean Networks As a Toy Model for the Brain
UNIVERSITY OF GENEVA SCIENCE FACULTY VRIJE UNIVERSITEIT OF AMSTERDAM PHYSICS SECTION Random Boolean Networks as a toy model for the brain MASTER THESIS presented at the science faculty of the University of Geneva for obtaining the Master in Theoretical Physics by Chlo´eB´eguin Supervisor (VU): Pr. Greg J Stephens Co-Supervisor (UNIGE): Pr. J´er^ome Kasparian July 2017 Contents Introduction1 1 Biology, physics and the brain4 1.1 Biological description of the brain................4 1.2 Criticality in the brain......................8 1.2.1 Physics reminder..................... 10 1.2.2 Experimental evidences.................. 15 2 Models of neural networks 20 2.1 Classes of models......................... 21 2.1.1 Spiking models...................... 21 2.1.2 Rate-based models.................... 23 2.1.3 Attractor networks.................... 24 2.1.4 Links between the classes of models........... 25 2.2 Random Boolean Networks.................... 28 2.2.1 General definition..................... 28 2.2.2 Kauffman network.................... 30 2.2.3 Hopfield network..................... 31 2.2.4 Towards a RBN for the brain.............. 32 2.2.5 The model......................... 33 3 Characterisation of RBNs 34 3.1 Attractors............................. 34 3.2 Damage spreading........................ 36 3.3 Canonical specific heat...................... 37 4 Results 40 4.1 One population with Gaussian weights............. 40 4.2 Dale's principle and balance of inhibition - excitation..... 46 4.3 Lognormal distribution of the weights.............. 51 4.4 Discussion............................. 55 i 5 Conclusion 58 Bibliography 60 Acknowledgements 66 A Python Code 67 A.1 Dynamics............................. 67 A.2 Attractor search.......................... 69 A.3 Hamming Distance........................ 73 A.4 Canonical specific heat..................... -
Boolean Analysis of MOS Circuits
Bo olean Analysis of MOS Circuits Randal E Bryant Computer Science Department CarnegieMellon University Pittsburgh PA February Abstract The switchlevel mo del represents a digital metaloxide semiconductor MOS cir cuit as a network of charge storage no des connected by resistive transistor switches The functionality of such a network can b e expressed as a series of systems of Bo olean equations Solving these equations symb olically yields a set of Bo olean formulas that describ e the mapping from input and current state to the new network state This analysis supp orts the same class of networks as the switchlevel simulator MOSSIM I I and provides the same functionality including the handling of bidirectional eects and indeterminate X logic values In the worst case the analysis of an n no de network can yield a set of formulas containing a total of O n op erations However all but a limited set of dense passtransistor networks give formulas with O n total op era tions The analysis can serve as the basis of ecient programs for a varietyoflogic design tasks including logic simulation on b oth conventional and sp ecial purp ose computers fault simulation test generation and symb olic verication Keywords and phrases switchlevel networks symb olic analysis logic simulation fault simulation simulation accelerators Intro duction The switchlevel mo del has proved successful as an abstract representation of digital metaloxide semiconductor MOS circuits for a variety of applications This mo del repre sents a circuit in terms of its exact transistor -
Percolation Theory Are Well-Suited To
Models of Disordered Media and Predictions of Associated Hydraulic Conductivity A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By L AARON BLANK B.S., Wright State University, 2004 2006 Wright State University WRIGHT STATE UNIVERSITY SCHOOL OF GRADUATE STUDIES Novermber 6, 2006 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY L Blank ENTITLED Models of Disordered Media and Predictions of Associated Hydraulic Conductivity BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science. _______________________ Allen Hunt, Ph.D. Thesis Advisor _______________________ Lok Lew Yan Voon, Ph.D. Department Chair _______________________ Joseph F. Thomas, Jr., Ph.D. Dean of the School of Graduate Studies Committee on Final Examination ____________________ Allen Hunt, Ph.D. ____________________ Brent D. Foy, Ph.D. ____________________ Gust Bambakidis, Ph.D. ____________________ Thomas Skinner, Ph.D. Abstract In the late 20th century there was a spill of Technetium in eastern Washington State at the US Department of Energy Hanford site. Resulting contamination of water supplies would raise serious health issues for local residents. Therefore, the ability to predict how these contaminants move through the soil is of great interest. The main contribution to contaminant transport arises from being carried along by flowing water. An important control on the movement of the water through the medium is the hydraulic conductivity, K, which defines the ease of water flow for a given pressure difference (analogous to the electrical conductivity). The overall goal of research in this area is to develop a technique which accurately predicts the hydraulic conductivity as well as its distribution, both in the horizontal and the vertical directions, for media representative of the Hanford subsurface. -
Submodular Hypergraphs: P-Laplacians, Cheeger Inequalities and Spectral Clustering
Submodular Hypergraphs: p-Laplacians, Cheeger Inequalities and Spectral Clustering Pan Li 1 Olgica Milenkovic 1 Abstract approximations have been based on the assumption that each hyperedge cut has the same weight, in which case the We introduce submodular hypergraphs, a family underlying hypergraph is termed homogeneous. of hypergraphs that have different submodular weights associated with different cuts of hyper- However, in image segmentation, MAP inference on edges. Submodular hypergraphs arise in cluster- Markov random fields (Arora et al., 2012; Shanu et al., ing applications in which higher-order structures 2016), network motif studies (Li & Milenkovic, 2017; Ben- carry relevant information. For such hypergraphs, son et al., 2016; Tsourakakis et al., 2017) and rank learn- we define the notion of p-Laplacians and derive ing (Li & Milenkovic, 2017), higher order relations between corresponding nodal domain theorems and k-way vertices captured by hypergraphs are typically associated Cheeger inequalities. We conclude with the de- with different cut weights. In (Li & Milenkovic, 2017), Li scription of algorithms for computing the spectra and Milenkovic generalized the notion of hyperedge cut of 1- and 2-Laplacians that constitute the basis of weights by assuming that different hyperedge cuts have new spectral hypergraph clustering methods. different weights, and that consequently, each hyperedge is associated with a vector of weights rather than a single scalar weight. If the weights of the hyperedge cuts are sub- 1. Introduction modular, then one can use a graph with nonnegative edge Spectral clustering algorithms are designed to solve a relax- weights to efficiently approximate the hypergraph, provided ation of the graph cut problem based on graph Laplacians that the largest size of a hyperedge is a relatively small con- that capture pairwise dependencies between vertices, and stant.