s-core network decomposition: a generalization of k-core analysis to weighted networks

Hyper-cores promote localization and efficient seeding in higher-order processes

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hypercoreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.

CLIPB4 Is a Central Node in the Protease Network that Regulates Humoral Immunity in Anopheles gambiae Mosquitoes

Insect humoral immune responses are regulated in part by protease cascades, whose components circulate as zymogens in the hemolymph. In mosquitoes, these cascades consist of clip-domain serine proteases (cSPs) and/or their non-catalytic homologs, which form a complex network, whose molecular make-up is not fully understood. Using a systems biology approach, based on a co-expression network of gene family members that function in melanization and co-immunoprecipitation using the serine protease inhibitor (SRPN)2, a key negative regulator of the melanization response in mosquitoes, we identify the cSP CLIPB4 from the African malaria mosquito Anopheles gambiae as a central node in this protease network. CLIPB4 is tightly co-expressed with SRPN2 and forms protein complexes with SRPN2 in the hemolymph of immune-challenged female mosquitoes. Genetic and biochemical approaches validate our network analysis and show that CLIPB4 is required for melanization and antibacterial immunity, acting as a prophenoloxidase (proPO)-activating protease, which is inhibited by SRPN2. In addition, we provide novel insight into the structural organization of the cSP network in An. gambiae, by demonstrating that CLIPB4 is able to activate proCLIPB8, a cSP upstream of the proPO-activating protease CLIPB9. These data provide the first evidence that, in mosquitoes, cSPs provide branching points in immune protease networks and deliver positive reinforcement in proPO activation cascades.

CLIPB4 is a central node in the protease network that regulates humoral immunity in Anopheles gambiae mosquitoes

Insect humoral immune responses are regulated in part by protease cascades, whose components circulate as zymogens in the hemolymph. In mosquitoes, these cascades consist of clip domain serine proteases (cSPs) and/or their non-catalytic homologs (cSPHs), which form a complex network, whose molecular make-up is not fully understood. Using a systems biology approach, based on a co-expression network of gene family members that function in melanization and co-immunoprecipitation using the serine protease inhibitor (SRPN)2, a key negative regulator of the melanization response in mosquitoes, we identify the cSP CLIPB4 from the African malaria mosquito Anopheles gambiae as a central node in this protease network. CLIPB4 is tightly co-expressed with SRPN2 and forms protein complexes with SRPN2 in the hemolymph of immune-challenged female mosquitoes. Genetic and biochemical approaches validate our network analysis and show that CLIPB4 is required for melanization and antibacterial immunity, acting as a prophenoloxidase (proPO)-activating protease, which is inhibited by SRPN2. In addition, we provide novel insight into the structural organization of the cSP network in An. gambiae, by demonstrating that CLIPB4 is able to activate proCLIPB8, a cSP upstream of the proPO-activating protease CLIPB9. These data provide the first evidence that, in mosquitoes, cSPs provide branching points in immune protease networks and deliver positive reinforcement in proPO activation cascades.

GeCoNet-Tool: a software package for gene co-expression network construction and analysis

BACKGROUND

Network analysis is a powerful tool for studying gene regulation and identifying biological processes associated with gene function. However, constructing gene co-expression networks can be a challenging task, particularly when dealing with a large number of missing values.

RESULTS

We introduce GeCoNet-Tool, an integrated gene co-expression network construction and analysis tool. The tool comprises two main parts: network construction and network analysis. In the network construction part, GeCoNet-Tool offers users various options for processing gene co-expression data derived from diverse technologies. The output of the tool is an edge list with the option of weights associated with each link. In network analysis part, the user can produce a table that includes several network properties such as communities, cores, and centrality measures. With GeCoNet-Tool, users can explore and gain insights into the complex interactions between genes.

Rigorous Criteria for the Collapse of Nonlinear Cooperative Networks

Many real-world complex systems, when hitting a tipping point, undergo irreversible sudden shifts that can eventually take a great toll on humanity and the natural world, such as ecosystem collapses, disease outbreaks, etc. Previous work has adopted approximations to predict the tipping points, but due to the nature of nonlinearity, this may lead to unexpected errors in predicting real-world systems. Here we obtain the rigorous bounds of the tipping points for general nonlinear cooperative networks. Our results offer two rigorous criteria that determine the collapse and survival of such a system. These two criteria are decided by the combined effect of dynamical parameters and interaction topology.

A robust core architecture of functional brain networks supports topological resilience and cognitive performance in middle- and old-aged adults

Aging is associated with gradual changes in cognition, yet some individuals exhibit protection against age-related cognitive decline. The topological characteristics of brain networks that promote protection against cognitive decline in aging are unknown. Here, we investigated whether the robustness and resilience of brain networks, queried via the delineation of the brain's core network structure, relate to age and cognitive performance in a cross-sectional dataset of healthy middle- and old-aged adults (n = 478, ages 40 to 90 y). First, we decomposed each subject's functional brain network using k-shell decomposition and found that age was negatively associated with robust core network structures. Next, we perturbed these networks, via attack simulations, and found that resilience of core brain network nodes also declined in relationship to age. We then partitioned our dataset into middle- (ages 40 to 65 y, n = 300) and old- (ages 65 to 90 y, n = 178) aged subjects and observed that older individuals had less robust core connectivity and resilience. Following these analyses, we found that episodic memory was positively related to robust connectivity and core resilience, particularly within the default node, limbic, and frontoparietal control networks. Importantly, we found that age-related differences in episodic memory were positively related to core resilience, which indicates a potential role for core resilience in protection against cognitive decline. Together, these findings suggest that robust core connectivity and resilience of brain networks could facilitate high cognitive performance in aging.

A global [Formula: see text] gene co-expression network constructed from hundreds of experimental conditions with missing values

BACKGROUND

Gene co-expression networks (GCNs) can be used to determine gene regulation and attribute gene function to biological processes. Different high throughput technologies, including one and two-channel microarrays and RNA-sequencing, allow evaluating thousands of gene expression data simultaneously, but these methodologies provide results that cannot be directly compared. Thus, it is complex to analyze co-expression relations between genes, especially when there are missing values arising for experimental reasons. Networks are a helpful tool for studying gene co-expression, where nodes represent genes and edges represent co-expression of pairs of genes.

RESULTS

In this paper, we establish a method for constructing a gene co-expression network for the Anopheles gambiae transcriptome from 257 unique studies obtained with different methodologies and experimental designs. We introduce the sliding threshold approach to select node pairs with high Pearson correlation coefficients. The resulting network, which we name AgGCN1.0, is robust to random removal of conditions and has similar characteristics to small-world and scale-free networks. Analysis of network sub-graphs revealed that the core is largely comprised of genes that encode components of the mitochondrial respiratory chain and the ribosome, while different communities are enriched for genes involved in distinct biological processes.

CONCLUSION

Analysis of the network reveals that both the architecture of the core sub-network and the network communities are based on gene function, supporting the power of the proposed method for GCN construction. Application of network science methodology reveals that the overall network structure is driven to maximize the integration of essential cellular functions, possibly allowing the flexibility to add novel functions.

Using Network Analysis and Machine Learning to Identify Virus Spread Trends in COVID-19

The outbreak of Coronavirus Disease 2019 (COVID-19) has infected and killed millions of people globally, resulting in a pandemic with enormous global impact. This disease affects the respiratory system, and the viral agent that causes it, SARS-CoV-2, spreads through droplets of saliva, as well as through coughing and sneezing. As an extremely transmissible viral infection, COVID-19 is causing significant damage to the economies of both developed and lower- and middle-income countries because of its direct impact on the health of citizens and the containment measures taken to curtail the virus. Methods to reduce or control the spread of the virus and protect the global population are needed to avoid further deaths, long-term health issues, and prolonged economic impact. The most effective approach to reduce viral spread and avoid a substantial collapse of the health system, in the absence of vaccines, is nonpharmaceutical interventions (NPI) such as enforcing social containment restrictions, monitoring overall population mobility, implementing widespread viral testing, and increasing hygiene measures. Our approach consists of combining network analytics with machine learning models by using a combination of anonymized health and telecommunications data to better understand the correlation between population movements and virus spread. This approach, called location network analysis (LNA), allows for accurate prediction of possible new outbreaks. It gives governments and health authorities a crucial tool that can help define more accurate public health metrics and can be used either to intensify social containment policies to avoid further spread or to ease them to reopen the economy. LNA can also help to retrospectively evaluate the effectiveness of policy responses to COVID-19.

Structural Features of the Human Connectome That Facilitate the Switching of Brain Dynamics via Noradrenergic Neuromodulation

The structural connectivity of human brain allows the coexistence of segregated and integrated states of activity. Neuromodulatory systems facilitate the transition between these functional states and recent computational studies have shown how an interplay between the noradrenergic and cholinergic systems define these transitions. However, there is still much to be known about the interaction between the structural connectivity and the effect of neuromodulation, and to what extent the connectome facilitates dynamic transitions. In this work, we use a whole brain model, based on the Jasen and Rit equations plus a human structural connectivity matrix, to find out which structural features of the human connectome network define the optimal neuromodulatory effects. We simulated the effect of the noradrenergic system as changes in filter gain, and studied its effects related to the global-, local-, and meso-scale features of the connectome. At the global-scale, we found that the ability of the network of transiting through a variety of dynamical states is disrupted by randomization of the connection weights. By simulating neuromodulation of partial subsets of nodes, we found that transitions between integrated and segregated states are more easily achieved when targeting nodes with greater connection strengths-local feature-or belonging to the rich club-meso-scale feature. Overall, our findings clarify how the network spatial features, at different levels, interact with neuromodulation to facilitate the switching between segregated and integrated brain states and to sustain a richer brain dynamics.

Identification of effective spreaders in contact networks using dynamical influence

Contact networks provide insights on disease spread due to the duration of close proximity interactions. For systems governed by consensus dynamics, network structure is key to optimising the spread of information. For disease spread over contact networks, the structure would be expected to be similarly influential. However, metrics that are essentially agnostic to the network's structure, such as weighted degree (strength) centrality and its variants, perform near-optimally in selecting effective spreaders. These degree-based metrics outperform eigenvector centrality, despite disease spread over a network being a random walk process. This paper improves eigenvector-based spreader selection by introducing the non-linear relationship between contact time and the probability of disease transmission into the assessment of network dynamics. This approximation of disease spread dynamics is achieved by altering the Laplacian matrix, which in turn highlights why nodes with a high degree are such influential disease spreaders. From this approach, a trichotomy emerges on the definition of an effective spreader where, for susceptible-infected simulations, eigenvector-based selections can either optimise the initial rate of infection, the average rate of infection, or produce the fastest time to full infection of the network. Simulated and real-world human contact networks are examined, with insights also drawn on the effective adaptation of ant colony contact networks to reduce pathogen spread and protect the queen ant.

Relevance of temporal cores for epidemic spread in temporal networks

Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To assess the relevance of such structures, we explore the effectiveness of strategies aimed either at containing or maximizing the impact of a spread, based respectively on removing span-cores of high cohesiveness or duration to decrease the epidemic risk, or on seeding the process from such structures. The effectiveness of such strategies is assessed in a variety of empirical data sets and compared to baselines that use only static information on the centrality of nodes and static concepts of coreness, as well as to a baseline based on a temporal centrality measure. Our results show that the most stable and cohesive temporal cores play indeed an important role in epidemic processes on temporal networks, and that their nodes are likely to include influential spreaders.

Identifying vital nodes in complex networks by adjacency information entropy

Identifying the vital nodes in networks is of great significance for understanding the function of nodes and the nature of networks. Many centrality indices, such as betweenness centrality (BC), eccentricity centrality (EC), closeness centricity (CC), structural holes (SH), degree centrality (DC), PageRank (PR) and eigenvector centrality (VC), have been proposed to identify the influential nodes of networks. However, some of these indices have limited application scopes. EC and CC are generally only applicable to undirected networks, while PR and VC are generally used for directed networks. To design a more applicable centrality measure, two vital node identification algorithms based on node adjacency information entropy are proposed in this paper. To validate the effectiveness and applicability of the proposed algorithms, contrast experiments are conducted with the BC, EC, CC, SH, DC, PR and VC indices in different kinds of networks. The results show that the index in this paper has a high correlation with the local metric DC, and it also has a certain correlation with the PR and VC indices for directed networks. In addition, the experimental results indicate that our algorithms can effectively identify the vital nodes in different networks.

Spatio-Temporal Change Characteristics of Spatial-Interaction Networks: Case Study within the Sixth Ring Road of Beijing, China

Spatial-interaction networks are an important factor in geography that could help in the exploration of both human spatial-temporal behavior and the structure of urban areas. This paper analyzes changes in the spatio-temporal characteristics of the Spatial-Interaction Networks of Beijing (SINB) in three consecutive steps. To begin with, we constructed 24 sequential snapshots of spatial population interactions on the basis of points of interest (POIs) collected from Dianping.com and various taxi GPS data in Beijing. Then, we used Jensen–Shannon distance and hierarchical clustering to integrate the 24 sequential network snapshots into four clusters. Finally, we improved the weighted k-core decomposition method by combining the complex network method and weighted distance in a geographic space. The results showed: (1) There are three layers in the SINB: a core layer, a bridge layer, and a periphery layer. The number of places greatly varies, and the SINB show an obvious hierarchical structure at different periods. The core layer contains fewer places that are between the Second and Fifth Ring Road in Beijing. Moreover, spatial distribution of places in the bridge layer is always in the same location as that of the core layer, and the quantity in the bridge layer is always superior to that in the core layer. The distributions of places in the periphery layer, however, are much greater and wider than the other two layers. (2) The SINB connected compactly over time, bearing much resemblance to a small-world network. (3) Two patterns of connection, each with different connecting ratios between layers, appear on weekdays and weekends, respectively. Our research plays a vital role in understanding urban spatial heterogeneity, and helps to support decisions in urban planning and traffic management.

Centrality-based identification of important edges in complex networks

Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different level of importance. We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis, as well as in evolving epileptic brain networks.

Network structure reveals patterns of legal complexity in human society: The case of the Constitutional legal network

Complexity in nature has been broadly found not only in physical and biological systems but also in social and economic systems. Although many studies have examined complex systems and helped us understand real-world complexity, the investigation to the legal complexity has not been thoroughly investigated. Here we introduce a novel approach to studying complex legal systems using complex network approaches. On the basis of the bipartite relations among Constitution articles and Court decisions, we built a complex legal network and found the system shows the heterogeneous structure as generally observed in many complex social systems. By treating legal networks as unique political regimes, we examine whether structural properties of the systems have been influenced as the society changes, or not. On one hand, there is a core structure in all legal networks regardless of any social circumstances. On the other hand, with relative comparison among different regimes' networks, we could identify characteristic structural properties that reveal their identity. Our analysis would contribute to provide a better understanding of legal complexity and practical guidelines for use in various legal and social applications.

Indirubin attenuates mouse psoriasis-like skin lesion in a CD274-dependent manner: an achievement of RNA sequencing

It was previously reported that the expression of CD274 was down-regulated in psoriatic epidermis, leading to immune disorders of psoriasis. However, the regulatory mechanisms of CD274 were rarely elucidated. We aimed to explore the regulatory mechanisms of CD274. Skin samples were collected from 18 patients with psoriasis vulgaris and 9 healthy participants for RNA sequencing. Candidate genes were chosen based on degree and k-core difference of genes in the co-expression network. The relations between candidate genes and CD274 were validated by flow cytometry and real-time PCR in primary human epidermal keratinocytes. The therapeutic effect of indirubin was assessed in an imiquimod-treated mouse model. Interferon-γ (IFN-γ), cyclin-dependent kinase (CDK) 1, Toll-like receptor 3 (TLR3), TLR4 and interleukin (IL)-17A were considered as candidate genes. In primary human epidermal keratinocytes, the level of CD274 was obviously increased under the stimulation of IFN-γ and CDK1 inhibitor (indirubin), independent of TLR4, TLR3 or IL-17A. Indirubin alleviated the severity of psoriatic mice in a CD274-dependent manner. Co-expression network analysis served as an effective method for the exploration of molecular mechanisms. We demonstrated for the first time that CD274 was the regulator of indirubin-mediated effect on mouse psoriasis-like skin lesion based on co-expression network analysis, contributing to the alleviation of mouse psoriasis-like skin lesion.

Big data analysis for evaluating bioinvasion risk

Background

Global maritime trade plays an important role in the modern transportation industry. It brings significant economic profit along with bioinvasion risk. Species translocate and establish in a non-native area through ballast water and biofouling. Aiming at aquatic bioinvasion issue, people proposed various suggestions for bioinvasion management. Nonetheless, these suggestions only focus on the chance of a port been affected but ignore the port’s ability to further spread the invaded species.

Results

To tackle the issues of the existing work, we propose a biosecurity triggering mechanism, where the bioinvasion risk of a port is estimated according to both the invaded risk of a port and its power of being a stepping-stone. To compute the invaded risk, we utilize the automatic identification system data, the ballast water data and marine environmental data. According to the invaded risk of ports, we construct a species invasion network (SIN). The incoming bioinvasion risk is derived from invaded risk data while the invasion risk spreading capability of each port is evaluated by s-core decomposition of SIN.

Conclusions

We illustrate 100 ports in the world that have the highest bioinvasion risk when the invaded risk and stepping-stone bioinvasion risk are equally treated. There are two bioinvasion risk intensive regions, namely the Western Europe (including the Western European margin and the Mediterranean) and the Asia-Pacific, which are just the region with a high growth rate of non-indigenous species and the area that has been identified as a source for many of non-indigenous species discovered elsewhere (especially the Asian clam, which is assumed to be the most invasive species worldwide).

Anatomy of an online misinformation network

Massive amounts of fake news and conspiratorial content have spread over social media before and after the 2016 US Presidential Elections despite intense fact-checking efforts. How do the spread of misinformation and fact-checking compete? What are the structural and dynamic characteristics of the core of the misinformation diffusion network, and who are its main purveyors? How to reduce the overall amount of misinformation? To explore these questions we built Hoaxy, an open platform that enables large-scale, systematic studies of how misinformation and fact-checking spread and compete on Twitter. Hoaxy captures public tweets that include links to articles from low-credibility and fact-checking sources. We perform k-core decomposition on a diffusion network obtained from two million retweets produced by several hundred thousand accounts over the six months before the election. As we move from the periphery to the core of the network, fact-checking nearly disappears, while social bots proliferate. The number of users in the main core reaches equilibrium around the time of the election, with limited churn and increasingly dense connections. We conclude by quantifying how effectively the network can be disrupted by penalizing the most central nodes. These findings provide a first look at the anatomy of a massive online misinformation diffusion network.

Structural stability of interaction networks against negative external fields

We explore structural stability of weighted and unweighted networks of positively interacting agents against a negative external field. We study how the agents support the activity of each other to confront the negative field, which suppresses the activity of agents and can lead to collapse of the whole network. The competition between the interactions and the field shape the structure of stable states of the system. In unweighted networks (uniform interactions) the stable states have the structure of k-cores of the interaction network. The interplay between the topology and the distribution of weights (heterogeneous interactions) impacts strongly the structural stability against a negative field, especially in the case of fat-tailed distributions of weights. We show that apart from critical slowing down there is also a critical change in the system structure that precedes the network collapse. The change can serve as an early warning of the critical transition. To characterize changes of network structure we develop a method based on statistical analysis of the k-core organization and so-called "corona" clusters belonging to the k-cores.

Surrogate-assisted identification of influences of network construction on evolving weighted functional networks

We aim at identifying factors that may affect the characteristics of evolving weighted networks derived from empirical observations. To this end, we employ various chains of analysis that are often used in field studies for a data-driven derivation and characterization of such networks. As an example, we consider fully connected, weighted functional brain networks before, during, and after epileptic seizures that we derive from multichannel electroencephalographic data recorded from epilepsy patients. For these evolving networks, we estimate clustering coefficient and average shortest path length in a time-resolved manner. Lastly, we make use of surrogate concepts that we apply at various levels of the chain of analysis to assess to what extent network characteristics are dominated by properties of the electroencephalographic recordings and/or the evolving weighted networks, which may be accessible more easily. We observe that characteristics are differently affected by the unavoidable referencing of the electroencephalographic recording, by the time-series-analysis technique used to derive the properties of network links, and whether or not networks were normalized. Importantly, for the majority of analysis settings, we observe temporal evolutions of network characteristics to merely reflect the temporal evolutions of mean interaction strengths. Such a property of the data may be accessible more easily, which would render the weighted network approach-as used here-as an overly complicated description of simple aspects of the data.

Comparative analysis of weighted gene co-expression networks in human and mouse

The application of complex network modeling to analyze large co-expression data sets has gained traction during the last decade. In particular, the use of the weighted gene co-expression network analysis framework has allowed an unbiased and systems-level investigation of genotype-phenotype relationships in a wide range of systems. Since mouse is an important model organism for biomedical research on human disease, it is of great interest to identify similarities and differences in the functional roles of human and mouse orthologous genes. Here, we develop a novel network comparison approach which we demonstrate by comparing two gene-expression data sets from a large number of human and mouse tissues. The method uses weighted topological overlap alongside the recently developed network-decomposition method of s-core analysis, which is suitable for making gene-centrality rankings for weighted networks. The aim is to identify globally central genes separately in the human and mouse networks. By comparing the ranked gene lists, we identify genes that display conserved or diverged centrality-characteristics across the networks. This framework only assumes a single threshold value that is chosen from a statistical analysis, and it may be applied to arbitrary network structures and edge-weight distributions, also outside the context of biology. When conducting the comparative network analysis, both within and across the two species, we find a clear pattern of enrichment of transcription factors, for the homeobox domain in particular, among the globally central genes. We also perform gene-ontology term enrichment analysis and look at disease-related genes for the separate networks as well as the network comparisons. We find that gene ontology terms related to regulation and development are generally enriched across the networks. In particular, the genes FOXE3, RHO, RUNX2, ALX3 and RARA, which are disease genes in either human or mouse, are on the top-10 list of globally central genes in the human and mouse networks.

A composite network of conserved and tissue specific gene interactions reveals possible genetic interactions in glioma

Differential co-expression network analyses have recently become an important step in the investigation of cellular differentiation and dysfunctional gene-regulation in cell and tissue disease-states. The resulting networks have been analyzed to identify and understand pathways associated with disorders, or to infer molecular interactions. However, existing methods for differential co-expression network analysis are unable to distinguish between various forms of differential co-expression. To close this gap, here we define the three different kinds (conserved, specific, and differentiated) of differential co-expression and present a systematic framework, CSD, for differential co-expression network analysis that incorporates these interactions on an equal footing. In addition, our method includes a subsampling strategy to estimate the variance of co-expressions. Our framework is applicable to a wide variety of cases, such as the study of differential co-expression networks between healthy and disease states, before and after treatments, or between species. Applying the CSD approach to a published gene-expression data set of cerebral cortex and basal ganglia samples from healthy individuals, we find that the resulting CSD network is enriched in genes associated with cognitive function, signaling pathways involving compounds with well-known roles in the central nervous system, as well as certain neurological diseases. From the CSD analysis, we identify a set of prominent hubs of differential co-expression, whose neighborhood contains a substantial number of genes associated with glioblastoma. The resulting gene-sets identified by our CSD analysis also contain many genes that so far have not been recognized as having a role in glioblastoma, but are good candidates for further studies. CSD may thus aid in hypothesis-generation for functional disease-associations.

Accurate ranking of influential spreaders in networks based on dynamically asymmetric link weights

We propose an efficient and accurate measure for ranking spreaders and identifying the influential ones in spreading processes in networks. While the edges determine the connections among the nodes, their specific role in spreading should be considered explicitly. An edge connecting nodes i and j may differ in its importance for spreading from i to j and from j to i. The key issue is whether node j, after infected by i through the edge, would reach out to other nodes that i itself could not reach directly. It becomes necessary to invoke two unequal weights w_{ij} and w_{ji} characterizing the importance of an edge according to the neighborhoods of nodes i and j. The total asymmetric directional weights originating from a node leads to a novel measure s_{i}, which quantifies the impact of the node in spreading processes. An s-shell decomposition scheme further assigns an s-shell index or weighted coreness to the nodes. The effectiveness and accuracy of rankings based on s_{i} and the weighted coreness are demonstrated by applying them to nine real-world networks. Results show that they generally outperform rankings based on the nodes' degree and k-shell index while maintaining a low computational complexity. Our work represents a crucial step towards understanding and controlling the spread of diseases, rumors, information, trends, and innovations in networks.

Super-Spreader Identification Using Meta-Centrality

Super-spreaders are the nodes of a network that can maximize their impacts on other nodes, e.g., in the case of information spreading or virus propagation. Many centrality measures have been proposed to identify such nodes from a given network. However, it has been observed that the identification accuracy based on those measures is not always satisfactory among different types of networks. In addition, the nodes identified by using single centrality are not always placed in the top section, where the super-spreaders are supposed to be, of the ranking generated by simulation. In this paper we take a meta-centrality approach by combining different centrality measures using a modified version of Borda count aggregation method. As a result, we are able to improve the performance of super-spreader identification for a broad range of real-world networks. While doing so, we discover a pattern in the centrality measures involved in the aggregation with respect to the topological structures of the networks used in the experiments. Further, we study the eigenvalues of the Laplacian matrix, also known as Laplacian spectrum, and by using the Earth Mover’s distance as a metric for the spectrum, we are able to identify four clusters to explain the aggregation results.

Improving the accuracy of the k-shell method by removing redundant links: From a perspective of spreading dynamics

Recent study shows that the accuracy of the k-shell method in determining node coreness in a spreading process is largely impacted due to the existence of core-like group, which has a large k-shell index but a low spreading efficiency. Based on the analysis of the structure of core-like groups in real-world networks, we discover that nodes in the core-like group are mutually densely connected with very few out-leaving links from the group. By defining a measure of diffusion importance for each edge based on the number of out-leaving links of its both ends, we are able to identify redundant links in the spreading process, which have a relatively low diffusion importance but lead to form the locally densely connected core-like group. After filtering out the redundant links and applying the k-shell method to the residual network, we obtain a renewed coreness k_s for each node which is a more accurate index to indicate its location importance and spreading influence in the original network. Moreover, we find that the performance of the ranking algorithms based on the renewed coreness are also greatly enhanced. Our findings help to more accurately decompose the network core structure and identify influential nodes in spreading processes.

Core-like groups result in invalidation of identifying super-spreader by k-shell decomposition

Identifying the most influential spreaders is an important issue in understanding and controlling spreading processes on complex networks. Recent studies showed that nodes located in the core of a network as identified by the k-shell decomposition are the most influential spreaders. However, through a great deal of numerical simulations, we observe that not in all real networks do nodes in high shells are very influential: in some networks the core nodes are the most influential which we call true core, while in others nodes in high shells, even the innermost core, are not good spreaders which we call core-like group. By analyzing the k-core structure of the networks, we find that the true core of a network links diversely to the shells of the network, while the core-like group links very locally within the group. For nodes in the core-like group, the k-shell index cannot reflect their location importance in the network. We further introduce a measure based on the link diversity of shells to effectively distinguish the true core and core-like group, and identify core-like groups throughout the networks. Our findings help to better understand the structural features of real networks and influential nodes.