Characterizing the interactions between classical and community-aware centrality measures in complex networks.
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ABSTRACT:
SUBMITTER: Rajeh S
PROVIDER: S-EPMC8115665 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:BackgroundCommunity structure is one of the key properties of complex networks and plays a crucial role in their topology and function. While an impressive amount of work has been done on the issue of community detection, very little attention has been so far devoted to the investigation of communities in real networks.Methodology/principal findingsWe present a systematic empirical analysis of the statistical properties of communities in large information, communication, technological, biological, and social networks. We find that the mesoscopic organization of networks of the same category is remarkably similar. This is reflected in several characteristics of community structure, which can be used as "fingerprints" of specific network categories. While community size distributions are always broad, certain categories of networks consist mainly of tree-like communities, while others have denser modules. Average path lengths within communities initially grow logarithmically with community size, but the growth saturates or slows down for communities larger than a characteristic size. This behaviour is related to the presence of hubs within communities, whose roles differ across categories. Also the community embeddedness of nodes, measured in terms of the fraction of links within their communities, has a characteristic distribution for each category.Conclusions/significanceOur findings, verified by the use of two fundamentally different community detection methods, allow for a classification of real networks and pave the way to a realistic modelling of networks' evolution.
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Project description:The roles of different nodes within a network are often understood through centrality analysis, which aims to quantify the capacity of a node to influence, or be influenced by, other nodes via its connection topology. Many different centrality measures have been proposed, but the degree to which they offer unique information, and whether it is advantageous to use multiple centrality measures to define node roles, is unclear. Here we calculate correlations between 17 different centrality measures across 212 diverse real-world networks, examine how these correlations relate to variations in network density and global topology, and investigate whether nodes can be clustered into distinct classes according to their centrality profiles. We find that centrality measures are generally positively correlated to each other, the strength of these correlations varies across networks, and network modularity plays a key role in driving these cross-network variations. Data-driven clustering of nodes based on centrality profiles can distinguish different roles, including topological cores of highly central nodes and peripheries of less central nodes. Our findings illustrate how network topology shapes the pattern of correlations between centrality measures and demonstrate how a comparative approach to network centrality can inform the interpretation of nodal roles in complex networks.
| S-EPMC6660088 | biostudies-literature
Project description:Numerous centrality measures have been developed to quantify the importances of nodes in time-independent networks, and many of them can be expressed as the leading eigenvector of some matrix. With the increasing availability of network data that changes in time, it is important to extend such eigenvector-based centrality measures to time-dependent networks. In this paper, we introduce a principled generalization of network centrality measures that is valid for any eigenvector-based centrality. We consider a temporal network with N nodes as a sequence of T layers that describe the network during different time windows, and we couple centrality matrices for the layers into a supra-centrality matrix of size NT × NT whose dominant eigenvector gives the centrality of each node i at each time t. We refer to this eigenvector and its components as a joint centrality, as it reflects the importances of both the node i and the time layer t. We also introduce the concepts of marginal and conditional centralities, which facilitate the study of centrality trajectories over time. We find that the strength of coupling between layers is important for determining multiscale properties of centrality, such as localization phenomena and the time scale of centrality changes. In the strong-coupling regime, we derive expressions for time-averaged centralities, which are given by the zeroth-order terms of a singular perturbation expansion. We also study first-order terms to obtain first-order-mover scores, which concisely describe the magnitude of nodes' centrality changes over time. As examples, we apply our method to three empirical temporal networks: the United States Ph.D. exchange in mathematics, costarring relationships among top-billed actors during the Golden Age of Hollywood, and citations of decisions from the United States Supreme Court.
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Project description:Numerous centrality measures have been introduced to identify "central" nodes in large networks. The availability of a wide range of measures for ranking influential nodes leaves the user to decide which measure may best suit the analysis of a given network. The choice of a suitable measure is furthermore complicated by the impact of the network topology on ranking influential nodes by centrality measures. To approach this problem systematically, we examined the centrality profile of nodes of yeast protein-protein interaction networks (PPINs) in order to detect which centrality measure is succeeding in predicting influential proteins. We studied how different topological network features are reflected in a large set of commonly used centrality measures.We used yeast PPINs to compare 27 common of centrality measures. The measures characterize and assort influential nodes of the networks. We applied principal component analysis (PCA) and hierarchical clustering and found that the most informative measures depend on the network's topology. Interestingly, some measures had a high level of contribution in comparison to others in all PPINs, namely Latora closeness, Decay, Lin, Freeman closeness, Diffusion, Residual closeness and Average distance centralities.The choice of a suitable set of centrality measures is crucial for inferring important functional properties of a network. We concluded that undertaking data reduction using unsupervised machine learning methods helps to choose appropriate variables (centrality measures). Hence, we proposed identifying the contribution proportions of the centrality measures with PCA as a prerequisite step of network analysis before inferring functional consequences, e.g., essentiality of a node.
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Project description:In order to understand and represent the importance of nodes within networks better, most of the studies that investigate graphs compute the nodes' centrality within their network(s) of interest. In the literature, the most frequent measures used are degree, closeness and/or betweenness centrality, even if other measures might be valid candidates for representing the importance of nodes within networks. The main contribution of this paper is the development of a methodology that allows one to understand, compare and validate centrality indices when studying a particular network of interest. The proposed methodology integrates the following steps: choosing the centrality measures for the network of interest; developing a theoretical taxonomy of these measures; identifying, by means of Principal Component Analysis (PCA), latent dimensions of centrality within the network of interest; verifying the proposed taxonomy of centrality measures; and identifying the centrality measures that best represent the network of interest. Also, we applied the proposed methodology to an existing graph of interest, in our case a real friendship student network. We chose eighteen centrality measures that were developed in SNA and are available and computed in a specific library (CINNA), defined them thoroughly, and proposed a theoretical taxonomy of these eighteen measures. PCA showed the emergence of six latent dimensions of centrality within the student network and saturation of most of the centrality indices on the same categories as those proposed by the theoretical taxonomy. Additionally, the results suggest that indices other than the ones most frequently applied might be more relevant for research on friendship student networks. Finally, the integrated methodology that we propose can be applied to other centrality indices and/or other network types than student graphs.
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Project description:Betweenness centrality is an indicator of a node's centrality in a network. It is equal to the number of shortest paths from all vertices to all others that pass through that node. Most of real-world large networks display a hierarchical community structure, and their betweenness computation possesses rather high complexity. Here we propose a new hierarchical decomposition approach to speed up the betweenness computation of complex networks. The advantage of this new method is its effective utilization of the local structural information from the hierarchical community. The presented method can significantly speed up the betweenness calculation. This improvement is much more evident in those networks with numerous homogeneous communities. Furthermore, the proposed method features a parallel structure, which is very suitable for parallel computation. Moreover, only a small amount of additional computation is required by our method, when small changes in the network structure are restricted to some local communities. The effectiveness of the proposed method is validated via the examples of two real-world power grids and one artificial network, which demonstrates that the performance of the proposed method is superior to that of the traditional method.
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Project description:The network theory of psychopathology suggests that symptoms in a disorder form a network and that identifying central symptoms within this network might be important for an effective and personalized treatment. However, recent evidence has been inconclusive. We analyzed contemporaneous idiographic networks of depression and anxiety symptoms. Two approaches were compared: a cascade-based attack where symptoms were deactivated in decreasing centrality order, and a normal attack where symptoms were deactivated based on original centrality estimates. Results showed that centrality measures significantly affected the attack's magnitude, particularly the number of components and average path length in both normal and cascade attacks. Degree centrality consistently had the highest impact on the network properties. This study emphasizes the importance of considering centrality measures when identifying treatment targets in psychological networks. Further research is needed to better understand the causal relationships and predictive capabilities of centrality measures in personalized treatments for mental disorders.
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Project description:A faithful modeling of real-world dynamical systems necessitates model evaluation. A recent promising methodological approach to this problem has been based on complex networks, which in turn have proven useful for the characterization of dynamical systems. In this context, we introduce three local network difference measures and demonstrate their capabilities in the field of climate modeling, where these measures facilitate a spatially explicit model evaluation.Building on a recent study by Feldhoff et al. [8] we comparatively analyze statistical and dynamical regional climate simulations of the South American monsoon system [corrected]. types of climate networks representing different aspects of rainfall dynamics are constructed from the modeled precipitation space-time series. Specifically, we define simple graphs based on positive as well as negative rank correlations between rainfall anomaly time series at different locations, and such based on spatial synchronizations of extreme rain events. An evaluation against respective networks built from daily satellite data provided by the Tropical Rainfall Measuring Mission 3B42 V7 reveals far greater differences in model performance between network types for a fixed but arbitrary climate model than between climate models for a fixed but arbitrary network type. We identify two sources of uncertainty in this respect. Firstly, climate variability limits fidelity, particularly in the case of the extreme event network; and secondly, larger geographical link lengths render link misplacements more likely, most notably in the case of the anticorrelation network; both contributions are quantified using suitable ensembles of surrogate networks. Our model evaluation approach is applicable to any multidimensional dynamical system and especially our simple graph difference measures are highly versatile as the graphs to be compared may be constructed in whatever way required. Generalizations to directed as well as edge- and node-weighted graphs are discussed.
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Project description:Residue interaction networks (RINs) describe a protein structure as a network of interacting residues. Central nodes in these networks, identified by centrality analyses, highlight those residues that play a role in the structure and function of the protein. However, little is known about the capability of such analyses to identify residues involved in the formation of macromolecular complexes. Here, we performed six different centrality measures on the RINs generated from the complexes of the SKEMPI 2 database of changes in protein-protein binding upon mutation in order to evaluate the capability of each of these measures to identify major binding residues. The analyses were performed with and without the crystallographic water molecules, in addition to the protein residues. We also investigated the use of a weight factor based on the inter-residue distances to improve the detection of these residues. We show that for the identification of major binding residues, closeness, degree, and PageRank result in good precision, whereas betweenness, eigenvector, and residue centrality analyses give a higher sensitivity. Including water in the analysis improves the sensitivity of all measures without losing precision. Applying weights only slightly raises the sensitivity of eigenvector centrality analysis. We finally show that a combination of multiple centrality analyses is the optimal approach to identify residues that play a role in protein-protein interaction.
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