Bianconi G 2003 The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed, focusing on the directed distance of nodes from the origin. The topology of the networks strongly depends on the dynamical parameter T, called the temperature. At T= infinity we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the network scales as the logarithm of the number of nodes in the network. At T=0 the two networks have an opposite behavior: the bosonic network remains very clusterized (the distance from the origin remains constant as the network increases the number of nodes), while the fermionic network grows following a single branch of the tree, and the distance from the origin varies as a power law of the number of nodes in the network. application/pdf https://sonar.ch/global/documents/123772 eng info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevE.67.056119 info:eu-repo/semantics/altIdentifier/pmid/12786232 info:eu-repo/semantics/openAccess Physical review. E, Statistical, nonlinear, and soft matter physics. - 2003 Size of quantum networks. http://purl.org/coar/resource_type/c_6501