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We propose high-order hypergraph walks as a framework to generalize graph-based network science techniques to hypergraphs. Edge incidence in hypergraphs is quantitative, yielding hypergraph walks with both length and width. Graph methods which then generalize to hypergraphs include connected component analyses, graph distance-based metrics such as closeness centrality, and motif-based measures such as clustering coefficients. We apply high-order analogs of these methods to real world hypernetworks, and show they reveal nuanced and interpretable structure that cannot be detected by graph-based methods. Lastly, we apply three generative models to the data and find that basic hypergraph properties, such as density and degree distributions, do not necessarily control these new structural measurements. Our work demonstrates how analyses of hypergraph-structured data are richer when utilizing tools tailored to capture hypergraph-native phenomena, and suggests one possible avenue towards that end.
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With great theoretical and practical significance, identifying the node spreading influence of complex network is one of the most promising domains. So far, various topology-based centrality measures have been proposed to identify the node spreading influence in a network. However, the node spreading influence is a result of the interplay between the network topology structure and spreading dynamics. In this paper, we build up the systematic method by combining the network structure and spreading dynamics to identify the node spreading influence. By combining the adjacent matrix $A$ and spreading parameter $beta$, we theoretical give the node spreading influence with the eigenvector of the largest eigenvalue. Comparing with the Susceptible-Infected-Recovered (SIR) model epidemic results for four real networks, our method could identify the node spreading influence more accurately than the ones generated by the degree, K-shell and eigenvector centrality. This work may provide a systematic method for identifying node spreading influence.
This work introduces an integrative approach based on Q-analysis with machine learning. The new approach, called Neural Hypernetwork, has been applied to a case study of pulmonary embolism diagnosis. The objective of the application of neural hyper-network to pulmonary embolism (PE) is to improve diagnose for reducing the number of CT-angiography needed. Hypernetworks, based on topological simplicial complex, generalize the concept of two-relation to many-body relation. Furthermore, Hypernetworks provide a significant generalization of network theory, enabling the integration of relational structure, logic and analytic dynamics. Another important results is that Q-analysis stays close to the data, while other approaches manipulate data, projecting them into metric spaces or applying some filtering functions to highlight the intrinsic relations. A pulmonary embolism (PE) is a blockage of the main artery of the lung or one of its branches, frequently fatal. Our study uses data on 28 diagnostic features of 1,427 people considered to be at risk of PE. The resulting neural hypernetwork correctly recognized 94% of those developing a PE. This is better than previous results that have been obtained with other methods (statistical selection of features, partial least squares regression, topological data analysis in a metric space).
In this work we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices are the statements and two statements are connected with a directed link if one statement is used to demonstrate the other one. We compare the obtained network with other directed acyclic graphs, such as a scientific citation network and a stochastic model. We also introduce a novel topological ordering for directed acyclic graphs and we discuss its properties in respect to the classical one. The main result is the observation that formal systems of knowledge topologically behave similarly to self-organised systems.
Background: Zipfs law and Heaps law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipfs law and the Heaps law motivates different understandings on the dependence between these two scalings, which is still hardly been clarified. Methodology/Principal Findings: In this article, we observe an evolution process of the scalings: the Zipfs law and the Heaps law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps law still exists with the disappearance of strict Zipfs law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States(U.S.) domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. Conclusions/Significance: The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipfs law and the Heaps law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.
Identifying influential spreaders is crucial for understanding and controlling spreading processes on social networks. Via assigning degree-dependent weights onto links associated with the ground node, we proposed a variant to a recent ranking algorithm named LeaderRank [L. Lv et al., PLoS ONE 6 (2011) e21202]. According to the simulations on the standard SIR model, the weighted LeaderRank performs better than LeaderRank in three aspects: (i) the ability to find out more influential spreaders, (ii) the higher tolerance to noisy data, and (iii) the higher robustness to intentional attacks.
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