Correlation in Complex Networks
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
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. -
Processes on Complex Networks. Percolation
Chapter 5 Processes on complex networks. Percolation 77 Up till now we discussed the structure of the complex networks. The actual reason to study this structure is to understand how this structure influences the behavior of random processes on networks. I will talk about two such processes. The first one is the percolation process. The second one is the spread of epidemics. There are a lot of open problems in this area, the main of which can be innocently formulated as: How the network topology influences the dynamics of random processes on this network. We are still quite far from a definite answer to this question. 5.1 Percolation 5.1.1 Introduction to percolation Percolation is one of the simplest processes that exhibit the critical phenomena or phase transition. This means that there is a parameter in the system, whose small change yields a large change in the system behavior. To define the percolation process, consider a graph, that has a large connected component. In the classical settings, percolation was actually studied on infinite graphs, whose vertices constitute the set Zd, and edges connect each vertex with nearest neighbors, but we consider general random graphs. We have parameter ϕ, which is the probability that any edge present in the underlying graph is open or closed (an event with probability 1 − ϕ) independently of the other edges. Actually, if we talk about edges being open or closed, this means that we discuss bond percolation. It is also possible to talk about the vertices being open or closed, and this is called site percolation. -
Network Science
NETWORK SCIENCE Random Networks Prof. Marcello Pelillo Ca’ Foscari University of Venice a.y. 2016/17 Section 3.2 The random network model RANDOM NETWORK MODEL Pál Erdös Alfréd Rényi (1913-1996) (1921-1970) Erdös-Rényi model (1960) Connect with probability p p=1/6 N=10 <k> ~ 1.5 SECTION 3.2 THE RANDOM NETWORK MODEL BOX 3.1 DEFINING RANDOM NETWORKS RANDOM NETWORK MODEL Network science aims to build models that reproduce the properties of There are two equivalent defini- real networks. Most networks we encounter do not have the comforting tions of a random network: Definition: regularity of a crystal lattice or the predictable radial architecture of a spi- der web. Rather, at first inspection they look as if they were spun randomly G(N, L) Model A random graph is a graph of N nodes where each pair (Figure 2.4). Random network theoryof nodes embraces is connected this byapparent probability randomness p. N labeled nodes are connect- by constructing networks that are truly random. ed with L randomly placed links. Erds and Rényi used From a modeling perspectiveTo a constructnetwork is a arandom relatively network simple G(N, object, p): this definition in their string consisting of only nodes and links. The real challenge, however, is to decide of papers on random net- where to place the links between1) the Start nodes with so thatN isolated we reproduce nodes the com- works [2-9]. plexity of a real system. In this 2)respect Select the a philosophynode pair, behindand generate a random a network is simple: We assume thatrandom this goal number is best betweenachieved by0 and placing 1. -
Fractal Network in the Protein Interaction Network Model
Journal of the Korean Physical Society, Vol. 56, No. 3, March 2010, pp. 1020∼1024 Fractal Network in the Protein Interaction Network Model Pureun Kim and Byungnam Kahng∗ Department of Physics and Astronomy, Seoul National University, Seoul 151-747 (Received 22 September 2009) Fractal complex networks (FCNs) have been observed in a diverse range of networks from the World Wide Web to biological networks. However, few stochastic models to generate FCNs have been introduced so far. Here, we simulate a protein-protein interaction network model, finding that FCNs can be generated near the percolation threshold. The number of boxes needed to cover the network exhibits a heavy-tailed distribution. Its skeleton, a spanning tree based on the edge betweenness centrality, is a scaffold of the original network and turns out to be a critical branching tree. Thus, the model network is a fractal at the percolation threshold. PACS numbers: 68.37.Ef, 82.20.-w, 68.43.-h Keywords: Fractal complex network, Percolation, Protein interaction network DOI: 10.3938/jkps.56.1020 I. INTRODUCTION consistent with that of the hub-repulsion model [2]. The fractal scaling of a FCN originates from the fractality of its skeleton underneath it [8]. The skeleton is regarded Fractal complex networks (FCNs) have been discov- as a critical branching tree: It exhibits a plateau in the ered in diverse real-world systems [1, 2]. Examples in- mean branching number functionn ¯(d), defined as the clude the co-authorship network [3], metabolic networks average number of offsprings created by nodes at a dis- [4], the protein interaction networks [5], the World-Wide tance d from the root. -
Neutral Evolution of Proteins: the Superfunnel in Sequence Space and Its Relation to Mutational Robustness
Neutral evolution of proteins: The superfunnel in sequence space and its relation to mutational robustness. Josselin Noirel, Thomas Simonson To cite this version: Josselin Noirel, Thomas Simonson. Neutral evolution of proteins: The superfunnel in sequence space and its relation to mutational robustness.. Journal of Chemical Physics, American Institute of Physics, 2008, 129 (18), pp.185104. 10.1063/1.2992853. hal-00488189 HAL Id: hal-00488189 https://hal-polytechnique.archives-ouvertes.fr/hal-00488189 Submitted on 22 May 2013 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THE JOURNAL OF CHEMICAL PHYSICS 129, 185104 ͑2008͒ Neutral evolution of proteins: The superfunnel in sequence space and its relation to mutational robustness Josselin Noirela͒ and Thomas Simonsonb͒ Laboratoire de Biochimie, École Polytechnique, Route de Saclay, Palaiseau 91128 Cedex, France ͑Received 31 July 2008; accepted 11 September 2008; published online 11 November 2008͒ Following Kimura’s neutral theory of molecular evolution ͓M. Kimura, The Neutral Theory of Molecular Evolution ͑Cambridge University Press, Cambridge, 1983͒͑reprinted in 1986͔͒,ithas become common to assume that the vast majority of viable mutations of a gene confer little or no functional advantage. Yet, in silico models of protein evolution have shown that mutational robustness of sequences could be selected for, even in the context of neutral evolution. -
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. -
Fractal Boundaries of Complex Networks
OFFPRINT Fractal boundaries of complex networks Jia Shao, Sergey V. Buldyrev, Reuven Cohen, Maksim Kitsak, Shlomo Havlin and H. Eugene Stanley EPL, 84 (2008) 48004 Please visit the new website www.epljournal.org TAKE A LOOK AT THE NEW EPL Europhysics Letters (EPL) has a new online home at www.epljournal.org Take a look for the latest journal news and information on: • reading the latest articles, free! • receiving free e-mail alerts • submitting your work to EPL www.epljournal.org November 2008 EPL, 84 (2008) 48004 www.epljournal.org doi: 10.1209/0295-5075/84/48004 Fractal boundaries of complex networks Jia Shao1(a),SergeyV.Buldyrev1,2, Reuven Cohen3, Maksim Kitsak1, Shlomo Havlin4 and H. Eugene Stanley1 1 Center for Polymer Studies and Department of Physics, Boston University - Boston, MA 02215, USA 2 Department of Physics, Yeshiva University - 500 West 185th Street, New York, NY 10033, USA 3 Department of Mathematics, Bar-Ilan University - 52900 Ramat-Gan, Israel 4 Minerva Center and Department of Physics, Bar-Ilan University - 52900 Ramat-Gan, Israel received 12 May 2008; accepted in final form 16 October 2008 published online 21 November 2008 PACS 89.75.Hc – Networks and genealogical trees PACS 89.75.-k – Complex systems PACS 64.60.aq –Networks Abstract – We introduce the concept of the boundary of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundary nodes seen from a given node of complex networks. We find that for both Erd˝os-R´enyi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. -
Giant Component in Random Multipartite Graphs with Given
Giant Component in Random Multipartite Graphs with Given Degree Sequences David Gamarnik ∗ Sidhant Misra † January 23, 2014 Abstract We study the problem of the existence of a giant component in a random multipartite graph. We consider a random multipartite graph with p parts generated according to a d given degree sequence ni (n) which denotes the number of vertices in part i of the multi- partite graph with degree given by the vector d. We assume that the empirical distribution of the degree sequence converges to a limiting probability distribution. Under certain mild regularity assumptions, we characterize the conditions under which, with high probability, there exists a component of linear size. The characterization involves checking whether the Perron-Frobenius norm of the matrix of means of a certain associated edge-biased distribu- tion is greater than unity. We also specify the size of the giant component when it exists. We use the exploration process of Molloy and Reed to analyze the size of components in the random graph. The main challenges arise due to the multidimensionality of the ran- dom processes involved which prevents us from directly applying the techniques from the standard unipartite case. In this paper we use techniques from the theory of multidimen- sional Galton-Watson processes along with Lyapunov function technique to overcome the challenges. 1 Introduction The problem of the existence of a giant component in random graphs was first studied by arXiv:1306.0597v3 [math.PR] 22 Jan 2014 Erd¨os and R´enyi. In their classical paper [ER60], they considered a random graph model on n and m edges where each such possible graph is equally likely. -
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. -
The Perceived Assortativity of Social Networks: Methodological Problems and Solutions
The perceived assortativity of social networks: Methodological problems and solutions David N. Fisher1, Matthew J. Silk2 and Daniel W. Franks3 Abstract Networks describe a range of social, biological and technical phenomena. An important property of a network is its degree correlation or assortativity, describing how nodes in the network associate based on their number of connections. Social networks are typically thought to be distinct from other networks in being assortative (possessing positive degree correlations); well-connected individuals associate with other well-connected individuals, and poorly-connected individuals associate with each other. We review the evidence for this in the literature and find that, while social networks are more assortative than non-social networks, only when they are built using group-based methods do they tend to be positively assortative. Non-social networks tend to be disassortative. We go on to show that connecting individuals due to shared membership of a group, a commonly used method, biases towards assortativity unless a large enough number of censuses of the network are taken. We present a number of solutions to overcoming this bias by drawing on advances in sociological and biological fields. Adoption of these methods across all fields can greatly enhance our understanding of social networks and networks in general. 1 1. Department of Integrative Biology, University of Guelph, Guelph, ON, N1G 2W1, Canada. Email: [email protected] (primary corresponding author) 2. Environment and Sustainability Institute, University of Exeter, Penryn Campus, Penryn, TR10 9FE, UK Email: [email protected] 3. Department of Biology & Department of Computer Science, University of York, York, YO10 5DD, UK Email: [email protected] Keywords: Assortativity; Degree assortativity; Degree correlation; Null models; Social networks Introduction Network theory is a useful tool that can help us explain a range of social, biological and technical phenomena (Pastor-Satorras et al 2001; Girvan and Newman 2002; Krause et al 2007). -
Social Network Analysis: Homophily
Social Network Analysis: homophily Donglei Du ([email protected]) Faculty of Business Administration, University of New Brunswick, NB Canada Fredericton E3B 9Y2 Donglei Du (UNB) Social Network Analysis 1 / 41 Table of contents 1 Homophily the Schelling model 2 Test of Homophily 3 Mechanisms Underlying Homophily: Selection and Social Influence 4 Affiliation Networks and link formation Affiliation Networks Three types of link formation in social affiliation Network 5 Empirical evidence Triadic closure: Empirical evidence Focal Closure: empirical evidence Membership closure: empirical evidence (Backstrom et al., 2006; Crandall et al., 2008) Quantifying the Interplay Between Selection and Social Influence: empirical evidence—a case study 6 Appendix A: Assortative mixing in general Quantify assortative mixing Donglei Du (UNB) Social Network Analysis 2 / 41 Homophily: introduction The material is adopted from Chapter 4 of (Easley and Kleinberg, 2010). "love of the same"; "birds of a feather flock together" At the aggregate level, links in a social network tend to connect people who are similar to one another in dimensions like Immutable characteristics: racial and ethnic groups; ages; etc. Mutable characteristics: places living, occupations, levels of affluence, and interests, beliefs, and opinions; etc. A.k.a., assortative mixing Donglei Du (UNB) Social Network Analysis 4 / 41 Homophily at action: racial segregation Figure: Credit: (Easley and Kleinberg, 2010) Donglei Du (UNB) Social Network Analysis 5 / 41 Homophily at action: racial segregation Credit: (Easley and Kleinberg, 2010) Figure: Credit: (Easley and Kleinberg, 2010) Donglei Du (UNB) Social Network Analysis 6 / 41 Homophily: the Schelling model Thomas Crombie Schelling (born 14 April 1921): An American economist, and Professor of foreign affairs, national security, nuclear strategy, and arms control at the School of Public Policy at University of Maryland, College Park. -
Social Support Networks Among Young Men and Transgender Women of Color Receiving HIV Pre-Exposure Prophylaxis
Journal of Adolescent Health 66 (2020) 268e274 www.jahonline.org Original article Social Support Networks Among Young Men and Transgender Women of Color Receiving HIV Pre-Exposure Prophylaxis Sarah Wood, M.D., M.S.H.P. a,b,*, Nadia Dowshen, M.D., M.S.H.P. a,b, José A. Bauermeister, M.P.H., Ph.D. c, Linden Lalley-Chareczko, M.A. d, Joshua Franklin a,b, Danielle Petsis, M.P.H. b, Meghan Swyryn d, Kezia Barnett, M.P.H. b, Gary E. Weissman, M.D., M.S.H.P. a, Helen C. Koenig, M.D., M.P.H. a,d, and Robert Gross, M.D., M.S.C.E. a,e a Perelman School of Medicine, University of Pennsylvania, Philadelphia, Pennsylvania b Division of Adolescent Medicine, Children's Hospital of Philadelphia, Philadelphia, Pennsylvania c School of Nursing, University of Pennsylvania, Philadelphia, Pennsylvania d Philadelphia FIGHT Community Health Centers, Philadelphia, Pennsylvania e Corporal Michael J. Crescenz VA Medical Center, Philadelphia, Pennsylvania Article history: Received May 13, 2019; Accepted August 1, 2019 Keywords: Pre-exposure prophylaxis; Social networks; Adherence; HIV; Adolescents ABSTRACT IMPLICATIONS AND CONTRIBUTION Purpose: The aim of the study was to characterize perceived social support for young men and transgender women who have sex with men (YM/TWSM) taking HIV pre-exposure prophylaxis This mixed-methods (PrEP). study of young men and Methods: Mixed-methods study of HIV-negative YM/TWSM of color prescribed oral PrEP. transgender women of Participants completed egocentric network inventories characterizing their social support color using pre-exposure fi ¼ networks and identifying PrEP adherence support gures.