Identifying critical higher-order interactions in complex networks

Diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, disease contagion between individuals, and cascading failures in power grids. The critical interactions in networks play critical roles in diffusion and primarily affect network structure and functions. While interactions can occur between two nodes as pairwise interactions, i.e., edges, they can also occur between three or more nodes, which are described as higher-order interactions. This report presents a novel method to identify critical higher-order interactions in complex networks. We propose two new Laplacians to generalize standard graph centrality measures for higher-order interactions. We then compare the performances of the generalized centrality measures using the size of giant component and the Susceptible-Infected-Recovered (SIR) simulation model to show the effectiveness of using higher-order interactions. We further compare them with the first-order interactions (i.e., edges). Experimental results suggest that higher-order interactions play more critical roles than edges based on both the size of giant component and SIR, and the proposed methods are promising in identifying critical higher-order interactions.

Bilateral Representation of Sensorimotor Responses in Benign Adult Familial Myoclonus Epilepsy: An MEG Study

Patients with cortical reflex myoclonus manifest typical neurophysiologic characteristics due to primary sensorimotor cortex (S1/M1) hyperexcitability, namely, contralateral giant somatosensory-evoked potentials/fields and a C-reflex (CR) in the stimulated arm. Some patients show a CR in both arms in response to unilateral stimulation, with about 10-ms delay in the non-stimulated compared with the stimulated arm. This bilateral C-reflex (BCR) may reflect strong involvement of bilateral S1/M1. However, the significance and exact pathophysiology of BCR within 50 ms are yet to be established because it is difficult to identify a true ipsilateral response in the presence of the giant component in the contralateral hemisphere. We hypothesized that in patients with BCR, bilateral S1/M1 activity will be detected using MEG source localization and interhemispheric connectivity will be stronger than in healthy controls (HCs) between S1/M1 cortices. We recruited five patients with cortical reflex myoclonus with BCR and 15 HCs. All patients had benign adult familial myoclonus epilepsy. The median nerve was electrically stimulated unilaterally. Ipsilateral activity was investigated in functional regions of interest that were determined by the N20m response to contralateral stimulation. Functional connectivity was investigated using weighted phase-lag index (wPLI) in the time-frequency window of 30–50 ms and 30–100 Hz. Among seven of the 10 arms of the patients who showed BCR, the average onset-to-onset delay between the stimulated and the non-stimulated arm was 8.4 ms. Ipsilateral S1/M1 activity was prominent in patients. The average time difference between bilateral cortical activities was 9.4 ms. The average wPLI was significantly higher in the patients compared with HCs in specific cortico-cortical connections. These connections included precentral-precentral, postcentral-precentral, inferior parietal (IP)-precentral, and IP-postcentral cortices interhemispherically (contralateral region-ipsilateral region), and precentral-IP and postcentral-IP intrahemispherically (contralateral region-contralateral region). The ipsilateral response in patients with BCR may be a pathologically enhanced motor response homologous to the giant component, which was too weak to be reliably detected in HCs. Bilateral representation of sensorimotor responses is associated with disinhibition of the transcallosal inhibitory pathway within homologous motor cortices, which is mediated by the IP. IP may play a role in suppressing the inappropriate movements seen in cortical myoclonus.

Identifying Influential Edges by Node Influence Distribution and Dissimilarity Strategy

Identifying influential edges in a complex network is a fundamental topic with a variety of applications. Considering the topological structure of networks, we propose an edge ranking algorithm DID (Dissimilarity Influence Distribution), which is based on node influence distribution and dissimilarity strategy. The effectiveness of the proposed method is evaluated by the network robustness R and the dynamic size of the giant component and compared with well-known existing metrics such as Edge Betweenness index, Degree Product index, Diffusion Intensity and Topological Overlap index in nine real networks and twelve BA networks. Experimental results show the superiority of DID in identifying influential edges. In addition, it is verified through experimental results that the effectiveness of Degree Product and Diffusion Intensity algorithm combined with node dissimilarity strategy has been effectively improved.

On Some Properties of Collaboration Graphs of Scientists in Math-Net.Ru

A study of two graphs of scientific cooperation based on co-authorship and citation according to the all-Russian mathematical portal was conducted Math-Net.Ru. A citation-based scientific collaboration graph is a directed graph without loops and multiple edges, whose vertices are the authors of publications, and arcs connect them when there is at least one publication of the first author that cites the publication of the second author. A co-authorship graph is an undirected graph in which the vertices are the authors, and the edges record the co-authorship of two authors in at least one article. The customary study of the main characteristics of both graphs is carried out: diameter and average distance, connectivity components and clustering. In both graphs, we observe a similar connectivity structure – the presence of a giant component and a large number of small components. The similarity and difference of scientific cooperation through co-authorship and citation is noted.

Analysing the Vulnerability of Public Transport Networks

This paper analyses the robustness of specific public transport networks. Common attributes and which of them have more influence on the networks’ vulnerability are established. Initially, the structural properties of the networks in two graphical representations (L-Space and P-Space) are checked. Afterwards, the spread of problems (traffic jams, etc.) are simulated, employing a model based on a propagation and recovery mechanism, similar to those used in the epidemiological processes. Next, the size of the largest connected subset of stops of the network (giant component) is measured. What is shown is that the faults randomly happened at stops or links, also displaying that those that occurred in the highest weighted links spread slower than others. These others appear at stops with the largest level of betweenness, degree, or eigenvector centralities and PageRank. The modification of the giant component, when several stops and links are removed, proves that the removal of stops with the highest interactive betweenness, PageRank, and degree centralities has the most significant influence on the network’s integrity. Some equivalences in the degree, betweenness, PageRank, and eigenvector centrality parameters have been found. All networks show high modularity with values of index Q close to 1. The networks with the highest assortativity and lowest average number of stops are the ones which a passenger can use to travel directly to their destination, without any change. The Molloy–Reed parameter is higher than 2 in all networks, demonstrating that high integrity exists in them. All stops were characterized by low k-cores ≤3.

Network Analysis for Economics and Finance: An Application to Firm Ownership

In this chapter, we introduce network analysis as an approach to model data in economics and finance. First, we review the most recent empirical applications using network analysis in economics and finance. Second, we introduce the main network metrics that are useful to describe the overall network structure and characterize the position of a specific node in the network. Third, we model information on firm ownership as a network: firms are the nodes while ownership relationships are the linkages. Data are retrieved from Orbis including information of millions of firms and their shareholders at worldwide level. We describe the necessary steps to construct the highly complex international ownership network. We then analyze its structure and compute the main metrics. We find that it forms a giant component with a significant number of nodes connected to each other. Network statistics show that a limited number of shareholders control many firms, revealing a significant concentration of power. Finally, we show how these measures computed at different levels of granularity (i.e., sector of activity) can provide useful policy insights.