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In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the…
Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…
We show that the protein-protein interaction networks can be surprisingly well described by a very simple evolution model of duplication and divergence. The model exhibits a remarkably rich behavior depending on a single parameter, the…
This paper examines the proximity of authors to those they cite using degrees of separation in a co-author network, essentially using collaboration networks to expand on the notion of self-citations. While the proportion of direct…
The exponential increase in the number of scientific publications raises the question of whether the sciences are expanding into a fractured structure, making cross-field communication difficult. On the other hand, scientists may be…
We demonstrate how sophisticated graph properties, such as small distances and scale-free degree distributions, arise naturally from a reinforcement mechanism on layered graphs. Every node is assigned an a-priori i.i.d. fitness with…
The rate at which nodes in evolving social networks acquire links (friends, citations) shows complex temporal dynamics. Preferential attachment and link copying models, while enabling elegant analysis, only capture rich-gets-richer effects,…
Many recent large-scale studies of interaction networks have focused on networks of accumulated contacts. In this paper we explore social networks of ongoing relationships with an emphasis on dynamical aspects. We find a distribution of…
In many growing networks, the age of the nodes plays an important role in deciding the attachment probability of the incoming nodes. For example, in a citation network, very old papers are seldom cited while recent papers are usually cited…
Distance correlation is a recent extension of Pearson's correlation, that characterises general statistical independence between Euclidean-space-valued random variables, not only linear relations. This review delves into how and when…
The area of networks is very interdisciplinary and exhibits many applications in several fields of science. Nevertheless, there are few studies focusing on geographically located $d$-dimensional networks. In this paper, we study scaling…
Link prediction in collaboration networks is often solved by identifying structural properties of existing nodes that are disconnected at one point in time, and that share a link later on. The maximally possible recall rate or upper bound…
In order to capture the effects of social ties in knowledge diffusion, this paper examines the publication network that emerges from the collaboration of researchers, using citation information as means to estimate knowledge flow. For this…
Findings: We show that the distance distribution in an undirected network Lorenz majorizes the one of a chain. As a consequence, the average and median distances in any such network are smaller than or equal to those of a chain. Research…
Research has shown that most resources shared in articles (e.g., URLs to code or data) are not kept up to date and mostly disappear from the web after some years (Zeng et al., 2019). Little is known about the factors that differentiate and…
We study the statistics of citations from all Physical Review journals for the 110-year period 1893 until 2003. In addition to characterizing the citation distribution and identifying publications with the highest citation impact, we…
In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear function of time but new links between…
We analyze time evolution of statistical distributions of citations to scientific papers published in one year. While these distributions can be fitted by a power-law dependence we find that they are nonstationary and the exponent of the…
Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…