Information on Price's Model

13.2 Within a set of papers on a particular topic it is found that the average paper cites 30 others in the set. Moreover the network of citations among the papers appears to be scale-free, with power-law exponent a = 3. Let us assume that the network is well described by the preferential attachment model of Price, discussed in Section 13.1. a) What is the average number of citations received by a paper? b) On average what fraction of papers receive no citations at all? c) On average what fraction of papers receive 100 or more citations? (p.436) Price's model of a citation network is as follows. Papers are published continually (though they do not have to be published at a constant rate) and newly appearing papers cite previously existing ones. As discussed in Section 3.2, the papers and citations form a directed citation network, the papers being the nodes and the citations being the directed edges between them. Since no paper ever disappears after it is published, nodes in this network are created but never destroyed. 13.2 Within a set of papers on a particular topic it is found that the average paper cites 30 others in the set. Moreover the network of citations among the papers appears to be scale-free, with power-law exponent a = 3. Let us assume that the network is well described by the preferential attachment model of Price, discussed in Section 13.1. a) What is the average number of citations received by a paper? b) On average what fraction of papers receive no citations at all? c) On average what fraction of papers receive 100 or more citations? (p.436) Price's model of a citation network is as follows. Papers are published continually (though they do not have to be published at a constant rate) and newly appearing papers cite previously existing ones. As discussed in Section 3.2, the papers and citations form a directed citation network, the papers being the nodes and the citations being the directed edges between them. Since no paper ever disappears after it is published, nodes in this network are created but never destroyed