Cture of numerous realworld networks YHO-13351 (free base) site creates situations for the “majority illusion
Cture of lots of realworld networks creates conditions for the “majority illusion” paradox.Components and MethodsWe used the configuration model [32, 33], as implemented by the SNAP library (https:snap. stanford.edudata) to make a scalefree network with a specified degree sequence. We generated a degree sequence from a power law of your type p(k)k. Right here, pk would be the fraction of nodes which have k halfedges. The configuration model proceeded by linking a pair of randomly selected halfedges to form an edge. The linking process was repeated till all halfedges have been made use of up or there were no far more strategies to kind 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 produce average degree related for the average degree in the scalefree networks.PLOS One DOI:0.37journal.pone.04767 February 7,three Majority IllusionTable . Network properties. Size of networks studied within this paper, as well as 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 5.26 46.64 two.76 20.04 29.two 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, including the collaboration network of higher 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 also 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 offers the probability that a randomly selected node in an undirected network has k neighbors (i.e degree k). This quantity also affects the probability that a randomly selected edge is connected to a node of degree k, otherwise known as neighbor degree distribution q(k). Because highdegree PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/23139739 nodes have extra edges, they’re going to be overrepresented in the neighbor degree distribution by a issue proportional to their degree; therefore, q(k) kp(k)hki, exactly where hki is the typical node degree. Networks generally have structure beyond that specified by their degree distribution: as an example, nodes may possibly preferentially link to others having a similar (or really distinctive) 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 chosen edge in an undirected network [35]. This quantity obeys normalization situations 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 involving degrees of connected nodes: ” ! X X 0 two 0 0 0 0 kk ; k q 2 kk e ; k hkiq : r kk 2 sq k;k0 sq k;k0 P P 2 Here, s2 k k2 q k kq . In assortative networks (rkk 0), nodes have a tendency q hyperlink to related nodes, e.g highdegree nodes to other highdegree nodes. In disassortative networks (rkk 0), alternatively, they prefer to link to dissimilar nodes. A star composed of a central hub and nodes linked only towards the hub is definitely an instance of a disassortative network. We can use Newman’s edge rewiring procedure [35] to change a network’s degree assort.