Corrected overlap weight and clustering coefficient

We discuss two well known network measures: the overlap weight of an edge and the clustering coefficient of a node. For both of them it turns out that they are not very useful for data analytic task to identify important elements (nodes or links) of a given network. The reason for this is that they attain their largest values on maximal subgraphs of relatively small size that are more probable to appear in a network than that of larger size. We show how the definitions of these measures can be corrected in such a way that they give the expected results. We illustrate the proposed corrected measures by applying them on the US Airports network using the program Pajek.Comment: The paper is a detailed and extended version of the talk presented at the CMStatistics (ERCIM) 2015 Conferenc

Information mobility in complex networks

The concept of information mobility in complex networks is introduced on the basis of a stochastic process taking place in the network. The transition matrix for this process represents the probability that the information arising at a given node is transferred to a target one. We use the fractional powers of this transition matrix to investigate the stochastic process at fractional time intervals. The mobility coefficient is then introduced on the basis of the trace of these fractional powers of the stochastic matrix. The fractional time at which a network diffuses 50% of the information contained in its nodes (1/ k50 ) is also introduced. We then show that the scale-free random networks display better spread of information than the non scale-free ones. We study 38 real-world networks and analyze their performance in spreading information from their nodes. We find that some real-world networks perform even better than the scale-free networks with the same average degree and we point out some of the structural parameters that make this possible

Avalanches in complex spin networks

We investigate the magnetization reversal processes on classes of complex spin networks with antiferromagnetic interaction along the network links. With slow field ramping the hysteresis loop and avalanches of spin flips occur due to topological inhomogeneity of the network, even without any disorder of the magnetic interaction [B. Tadic, et al., Phys. Rev. Lett. 94 (2005) 137204]. Here we study in detail properties of the magnetization avalanches, hysteresis curves and density of domain walls and show how they can be related to the structural inhomogeneity of the network. The probability distribution of the avalanche size, N_s(s), displays the power-law behaviour for small s, i.e. N_s(s)\propto s^{-\alpha}. For the scale-free networks, grown with preferential attachment, \alpha increases with the connectivity parameter M from 1.38 for M=1 (trees) to 1.52 for M=25. For the exponential networks, \alpha is close to 1.0 in the whole range of M.Comment: 16 pages, 10 figures in 29 eps file

Guiding equitable prioritisation of COVID-19 vaccine distribution and strategic deployment in South Africa to enhance effectiveness and access to vulnerable communities and prevent waste

BACKGROUND. In South Africa (SA), >2.4 million cases of COVID 19 and >72 000 deaths were recorded between March 2020 and 1 August 2021, affecting the country’s 52 districts to various extents. SA has committed to a COVID 19 vaccine roll-out in three phases, prioritising frontline workers, the elderly, people with comorbidities and essential workers. However, additional actions will be necessary to support efficient allocation and equitable access for vulnerable, access-constrained communities. OBJECTIVES. To explore various determinants of disease severity, resurgence risk and accessibility in order to aid an equitable, effective vaccine roll-out for SA that would maximise COVID 19 epidemic control by reducing the number of COVID 19 transmissions and resultant deaths, while at the same time reducing the risk of vaccine wastage. METHODS. For the 52 districts of SA, 26 COVID 19 indicators such as hospital admissions, deaths in hospital and mobility were ranked and hierarchically clustered with cases to identify which indicators can be used as indicators for severity or resurgence risk. Districts were then ranked using the estimated COVID 19 severity and resurgence risk to assist with prioritisation of vaccine roll-out. Urban and rural accessibility were also explored as factors that could limit vaccine roll-out in hard-to-reach communities. RESULTS. Highly populated urban districts showed the most cases. Districts such as Buffalo City, City of Cape Town and Nelson Mandela Bay experienced very severe first and second waves of the pandemic. Districts with high mobility, population size and density were found to be at highest risk of resurgence. In terms of accessibility, we found that 47.2% of the population are within 5 km of a hospital with ≥50 beds, and this percentage ranged from 87.0% in City of Cape Town to 0% in Namakwa district. CONCLUSIONS. The end goal is to provide equal distribution of vaccines proportional to district populations, which will provide fair protection. Districts with a high risk of resurgence and severity should be prioritised for vaccine roll-out, particularly the major metropolitan areas. We provide recommendations for allocations of different vaccine types for each district that consider levels of access, numbers of doses and cold-chain storage capability.The American people through the United States Agency for International Development (USAID).http://www.samj.org.zadm2022Human Nutritio