We consider degree-biased random walkers whose probability to move from a node to one of its neighbors of degree k is proportional to k α , where α is a tuning parameter. We study both numerically and analytically three types of characteristic times, namely: i) the time the walker needs to come back to the starting node, ii) the time it takes to visit a given node for the first time, and iii) the time it takes to visit all the nodes of the network. We consider a large data set of real-world networks and we show that the value of α which minimizes the three characteristic times is different from the value αmin = −1 analytically found for uncorrelated networks in the mean-field approximation. In addition to this, we found that assortative networks have preferentially a value of αmin in the range [−1, −0.5], while disassortative networks have αmin in the range [−0.5, 0]. We derive an analytical relation between the degree correlation exponent ν and the optimal bias value αmin, which works well for real-world assortative networks. When only local information is available, degree-biased random walks can guarantee smaller characteristic times than the classical unbiased random walks, by means of an appropriate tuning of the motion bias.PACS numbers: 89.75. Hc, 05.40.Fb, 89.75.Kd In the last decade or so the quantitative analysis of networks having different origin and function, including social networks, the human brain, the Internet, the World Wide Web, has revealed that all these systems exhibit comparable structural properties at different scales, and are more similar to each other than expected [1,2]. It has been found that the structural complexity of networks from the real world usually has a significant impact on the dynamical processes occurring over them, including opinion dynamics [3], epidemics [4] and synchronization [5].Random walks are the simplest way to explore a network, and are one of the most widely studied class of processes on complex networks [6,7]. Different kinds of random walks have been used to implement efficient local search strategies [8,9], and also to reveal the presence of hierarchies and network communities [10,11]. Particular attention has been devoted to the study of the characteristic times associated to random walks, such as the mean return times, or the mean first passage times, respectively the average time the walker takes to come back to the starting node or to hit a given node [12]. Such characteristic times can be determined analytically for random walks on regular lattices [13], but their calculation for graphs with heterogeneous structures is still the object of active research [14,15]. Recent results include the derivation of analytic expressions for the characteristic times of unbiased random walks on Erdös-Rényi random graphs [16], on fractal networks [17][18][19][20] and on particular classes of scale-free graphs [21]. To date, only approximate solutions are available for random walks on real networks [22][23][24][25].A class of random walks which is particularly int...
5 Complexity Science Hub Vienna (CSHV), Vienna (Austria) † M.B. and V.C. contributed equally to this work. By drawing on large-scale online data we construct and analyze the timevarying worldwide network of professional relationships among start-ups. The nodes of this network represent companies, while the links model the flow of employees and the associated transfer of know-how across companies. We use network centrality measures to assess, at an early stage, the likelihood of the long-term positive performance of a start-up, showing that the start-up network has predictive power and provides valuable recommendations doubling the current state of the art performance of venture funds. Our network-based approach not only offers an effective alternative to the labour-intensive screening processes of venture capital firms, but can also enable entrepreneurs and policy-makers to conduct a more objective assessment of the long-term potentials of innovation ecosystems and to target interventions accordingly. Recent years have witnessed an unprecedented growth of interest in start-up companies. Policy-1 arXiv:1904.08171v1 [physics.soc-ph]
Citation networks have been widely used to study the evolution of science through the lenses of the underlying patterns of knowledge flows among academic papers, authors, research sub-fields, and scientific journals. Here we focus on citation networks to cast light on the salience of homophily, namely the principle that similarity breeds connection, for knowledge transfer between papers. To this end, we assess the degree to which citations tend to occur between papers that are concerned with seemingly related topics or research problems. Drawing on a large data set of articles published in the journals of the American Physical Society between 1893 and 2009, we propose a novel method for measuring the similarity between articles through the statistical validation of the overlap between their bibliographies. Results suggest that the probability of a citation made by one article to another is indeed an increasing function of the similarity between the two articles. Our study also enables us to uncover missing citations between pairs of highly related articles, and may thus help identify barriers to effective knowledge flows. By quantifying the proportion of missing citations, we conduct a comparative assessment of distinct journals and research sub-fields in terms of their ability to facilitate or impede the dissemination of knowledge. Findings indicate that Electromagnetism and Interdisciplinary Physics are the two sub-fields in physics with the smallest percentage of missing citations. Moreover, knowledge transfer seems to be more effectively facilitated by journals of wide visibility, such as Physical Review Letters, than by lower-impact ones. Our study has important implications for authors, editors and reviewers of scientific journals, as well as public preprint repositories, as it provides a procedure for recommending relevant yet missing references and properly integrating bibliographies of papers.
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