Cture of several realworld networks creates situations for the 'majority illusionCture of numerous

Cture of several realworld networks creates situations for the “majority illusion
Cture of numerous realworld networks creates conditions for the “majority illusion” paradox.Supplies and MethodsWe utilized the configuration model [32, 33], as implemented by the SNAP library (https:snap. stanford.edudata) to create a scalefree network with a specified degree sequence. We generated a degree sequence from a energy law from the kind p(k)k. Right here, pk may be the fraction of nodes that have k halfedges. The configuration model proceeded by linking a pair of randomly selected halfedges to type an edge. The linking procedure was repeated till all halfedges have already been employed up or there had been no more ways to type an edge. To make ErdsR yitype networks, we started with N 0,000 nodes and linked pairs at random with some fixed probability. These probabilities had been selected to generate average degree comparable towards the average degree from the scalefree networks.PLOS One DOI:0.37journal.pone.04767 February 7,three Majority IllusionTable . Network properties. Size of networks studied within this paper, in conjunction with their typical degree hki and degree assortativity coefficient rkk. network HepTh Reactome Digg Enron Twitter Political blogs nodes 9,877 six,327 27,567 36,692 23,025 ,490 edges 25,998 47,547 75,892 367,662 336,262 9,090 hki five.26 46.64 two.76 20.04 29.2 25.62 rkk 0.2679 0.249 0.660 0.08 0.375 0.doi:0.37journal.pone.04767.tThe statistics of realworld networks we studied, such as the MedChemExpress Ceruletide collaboration network of high power physicist (HepTh), Human protein rotein interactions network from Reactome project (http:reactome.orgpagesdownloaddata), Digg follower graph (DOI:0.6084 m9.figshare.2062467), Enron e mail network (http:cs.cmu.eduenron), Twitter user voting graph [34], and a network of political blogs (http:wwwpersonal.umich.edumejn netdata) are summarized in Table .ResultsA network’s structure is partly specified by its degree distribution p(k), which provides the probability that a randomly chosen node in an undirected network has k neighbors (i.e degree k). This quantity also impacts the probability that a randomly chosen edge is connected to a node of degree k, otherwise called neighbor degree distribution q(k). Due to the fact highdegree PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/23139739 nodes have more edges, they’ll be overrepresented in the neighbor degree distribution by a element proportional to their degree; therefore, q(k) kp(k)hki, exactly where hki would be the typical node degree. Networks usually have structure beyond that specified by their degree distribution: for instance, nodes could preferentially hyperlink to other individuals with a equivalent (or quite diverse) degree. Such degree correlation is captured by the joint degree distribution e(k, k0 ), the probability to locate nodes of degrees k and k0 at either finish of a randomly selected edge in an undirected network [35]. This quantity obeys normalization conditions kk0 e(k, k0 ) and k0 e(k, k0 ) q(k). Globally, degree correlation in an undirected network is quantified by the assortativity coefficient, which can be just the Pearson correlation among degrees of connected nodes: ” ! X X 0 two 0 0 0 0 kk ; k q two kk e ; k hkiq : r kk two sq k;k0 sq k;k0 P P two Here, s2 k k2 q k kq . In assortative networks (rkk 0), nodes possess a tendency q hyperlink to comparable nodes, e.g highdegree nodes to other highdegree nodes. In disassortative networks (rkk 0), on the other hand, they choose to link to dissimilar nodes. A star composed of a central hub and nodes linked only towards the hub is definitely an example of a disassortative network. We are able to use Newman’s edge rewiring procedure [35] to modify a network’s degree assort.