Efficiently counting complex multilayer temporal motifs in large-scale networks

Abstract This paper proposes novel algorithms for efficiently counting complex network motifs in dynamic networks that are changing over time. Network motifs are small characteristic configurations of a few nodes and edges, and have repeatedly been shown to provide insightful information for understanding the meso-level structure of a network. Here, we deal with counting more complex temporal motifs in large-scale networks that may consist of millions of nodes and edges. The first contribution is an efficient approach to count temporal motifs in multilayer networks and networks with partial timing, two prevalent aspects of many real-world complex networks. We analyze the complexity of these algorithms and empirically validate their performance on a number of real-world user communication networks extracted from online knowledge exchange platforms. Among other things, we find that the multilayer aspects provide significant insights in how complex user interaction patterns differ substantially between online platforms. The second contribution is an analysis of the viability of motif counting algorithms for motifs that are larger than the triad motifs studied in previous work. We provide a novel categorization of motifs of size four, and determine how and at what computational cost these motifs can still be counted efficiently. In doing so, we delineate the “computational frontier” of temporal motif counting algorithms.

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Automated monitoring of behavior reveals bursty interaction patterns and rapid spreading dynamics in honeybee social networks

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.1713568115 ◽

2018 ◽

Vol 115 (7) ◽

pp. 1433-1438 ◽

Cited By ~ 49

Author(s):

Tim Gernat ◽

Vikyath D. Rao ◽

Martin Middendorf ◽

Harry Dankowicz ◽

Nigel Goldenfeld ◽

...

Keyword(s):

Social Networks ◽

Social Interactions ◽

Communication Networks ◽

Disease Transmission ◽

Large Scale ◽

Reference Network ◽

Interaction Patterns ◽

Human Communication ◽

Automated Monitoring ◽

Phone Calls

Social networks mediate the spread of information and disease. The dynamics of spreading depends, among other factors, on the distribution of times between successive contacts in the network. Heavy-tailed (bursty) time distributions are characteristic of human communication networks, including face-to-face contacts and electronic communication via mobile phone calls, email, and internet communities. Burstiness has been cited as a possible cause for slow spreading in these networks relative to a randomized reference network. However, it is not known whether burstiness is an epiphenomenon of human-specific patterns of communication. Moreover, theory predicts that fast, bursty communication networks should also exist. Here, we present a high-throughput technology for automated monitoring of social interactions of individual honeybees and the analysis of a rich and detailed dataset consisting of more than 1.2 million interactions in five honeybee colonies. We find that bees, like humans, also interact in bursts but that spreading is significantly faster than in a randomized reference network and remains so even after an experimental demographic perturbation. Thus, while burstiness may be an intrinsic property of social interactions, it does not always inhibit spreading in real-world communication networks. We anticipate that these results will inform future models of large-scale social organization and information and disease transmission, and may impact health management of threatened honeybee populations.

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Fast Change Point Detection on Dynamic Social Networks

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2017/417 ◽

2017 ◽

Cited By ~ 10

Author(s):

Yu Wang ◽

Aniket Chakrabarti ◽

David Sivakoff ◽

Srinivasan Parthasarathy

Keyword(s):

Communication Networks ◽

Real World ◽

Change Point ◽

Dynamic Networks ◽

Change Point Detection ◽

Logical Time ◽

Dynamic Social Networks ◽

Fast Change ◽

Time Stamps ◽

Point Detection

A number of real world problems in many domains (e.g. sociology, biology, political science and communication networks) can be modeled as dynamic networks with nodes representing entities of interest and edges representing interactions among the entities at different points in time. A common representation for such models is the snapshot model - where a network is defined at logical time-stamps. An important problem under this model is change point detection. In this work we devise an effective and efficient three-step-approach for detecting change points in dynamic networks under the snapshot model. Our algorithm achieves up to 9X speedup over the state-of-the-art while improving quality on both synthetic and real world networks.

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Network Patterns of Herbal Combinations in Traditional Chinese Clinical Prescriptions

Frontiers in Pharmacology ◽

10.3389/fphar.2020.590824 ◽

2021 ◽

Vol 11 ◽

Author(s):

Ning Wang ◽

Ninglin Du ◽

Yonghong Peng ◽

Kuo Yang ◽

Zixin Shu ◽

...

Keyword(s):

Real World ◽

Large Scale ◽

Low Frequency ◽

Network Pharmacology ◽

Clinical Settings ◽

Interaction Patterns ◽

Very High Frequency ◽

Network Patterns ◽

Herbal Prescription ◽

Very High

As a well-established multidrug combinations schema, traditional Chinese medicine (herbal prescription) has been used for thousands of years in real-world clinical settings. This paper uses a complex network approach to investigate the regularities underlying multidrug combinations in herbal prescriptions. Using five collected large-scale real-world clinical herbal prescription datasets, we construct five weighted herbal combination networks with herb as nodes and herbal combinational use in herbal prescription as links. We found that the weight distribution of herbal combinations displays a clear power law, which means that most herb pairs were used in low frequency and some herb pairs were used in very high frequency. Furthermore, we found that it displays a clear linear negative correlation between the clustering coefficients and the degree of nodes in the herbal combination network (HCNet). This indicates that hierarchical properties exist in the HCNet. Finally, we investigate the molecular network interaction patterns between herb related target modules (i.e., subnetworks) in herbal prescriptions using a network-based approach and further explore the correlation between the distribution of herb combinations and prescriptions. We found that the more the hierarchical prescription, the better the corresponding effect. The results also reflected a well-recognized principle called “Jun-Chen-Zuo-Shi” in TCM formula theories. This also gives references for multidrug combination development in the field of network pharmacology and provides the guideline for the clinical use of combination therapy for chronic diseases.

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A simple differential geometry for complex networks

Network Science ◽

10.1017/nws.2020.42 ◽

2020 ◽

pp. 1-28

Author(s):

Emil Saucan ◽

Areejit Samal ◽

Jürgen Jost

Keyword(s):

Differential Geometry ◽

Complex Networks ◽

Ricci Curvature ◽

Real World ◽

Large Scale ◽

Metric Spaces ◽

Geodesic Curvature ◽

Higher Dimensional ◽

Large Scale Networks ◽

Bonnet Theorem

Abstract We introduce new definitions of sectional, Ricci, and scalar curvatures for networks and their higher dimensional counterparts, derived from two classical notions of curvature for curves in general metric spaces, namely, the Menger curvature and the Haantjes curvature. These curvatures are applicable to unweighted or weighted and undirected or directed networks and are more intuitive and easier to compute than other network curvatures. In particular, the proposed curvatures based on the interpretation of Haantjes definition as geodesic curvature allow us to give a network analogue of the classical local Gauss–Bonnet theorem. Furthermore, we propose even simpler and more intuitive proxies for the Haantjes curvature that allow for even faster and easier computations in large-scale networks. In addition, we also investigate the embedding properties of the proposed Ricci curvatures. Lastly, we also investigate the behavior, both on model and real-world networks, of the curvatures introduced herein with more established notions of Ricci curvature and other widely used network measures.

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SepNE: Bringing Separability to Network Embedding

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33014261 ◽

2019 ◽

Vol 33 ◽

pp. 4261-4268 ◽

Cited By ~ 2

Author(s):

Ziyao Li ◽

Liang Zhang ◽

Guojie Song

Keyword(s):

Large Scale ◽

State Of The Art ◽

Dynamic Networks ◽

Distributed Learning ◽

Network Embedding ◽

Large Networks ◽

Comparable Accuracy ◽

Large Scale Networks ◽

Low Dimensional ◽

Almost All

Many successful methods have been proposed for learning low dimensional representations on large-scale networks, while almost all existing methods are designed in inseparable processes, learning embeddings for entire networks even when only a small proportion of nodes are of interest. This leads to great inconvenience, especially on super-large or dynamic networks, where these methods become almost impossible to implement. In this paper, we formalize the problem of separated matrix factorization, based on which we elaborate a novel objective function that preserves both local and global information. We further propose SepNE, a simple and flexible network embedding algorithm which independently learns representations for different subsets of nodes in separated processes. By implementing separability, our algorithm reduces the redundant efforts to embed irrelevant nodes, yielding scalability to super-large networks, automatic implementation in distributed learning and further adaptations. We demonstrate the effectiveness of this approach on several real-world networks with different scales and subjects. With comparable accuracy, our approach significantly outperforms state-of-the-art baselines in running times on large networks.

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Algorithms for generating large-scale clustered random graphs

Network Science ◽

10.1017/nws.2014.7 ◽

2014 ◽

Vol 2 (3) ◽

pp. 403-415 ◽

Cited By ~ 4

Author(s):

CHENG WANG ◽

OMAR LIZARDO ◽

DAVID HACHEN

Keyword(s):

Random Graph ◽

Random Graphs ◽

Real World ◽

Local Structure ◽

Topological Structure ◽

Large Scale ◽

Random Processes ◽

Clustering Coefficient ◽

Computation Efficiency ◽

Large Scale Networks

AbstractReal-world networks are often compared to random graphs to assess whether their topological structure could be a result of random processes. However, a simple random graph in large scale often lacks social structure beyond the dyadic level. As a result we need to generate clustered random graph to compare the local structure at higher network levels. In this paper a generalized version of Gleeson's algorithm G(VS, VT, ES, ET, S, T) is advanced to generate a clustered random graph in large-scale which persists the number of vertices |V|, the number of edges |E|, and the global clustering coefficient CΔ as in the real network and it works successfully for nine large-scale networks. Our new algorithm also has advantages in randomness evaluation and computation efficiency when compared with the existing algorithms.

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Local dependency in networks

International Journal of Applied Mathematics and Computer Science ◽

10.1515/amcs-2015-0022 ◽

2015 ◽

Vol 25 (2) ◽

pp. 281-293 ◽

Cited By ~ 6

Author(s):

Miloš Kudĕlka ◽

Šárka Zehnalová ◽

Zdenĕk Horák ◽

Pavel Krömer ◽

Václav Snášel

Keyword(s):

Real World ◽

Large Scale ◽

Real World Data ◽

High Quality ◽

High Effectiveness ◽

Local Dependency ◽

Node Ranking ◽

Large Scale Networks ◽

The Relationship ◽

Entire Network

Abstract Many real world data and processes have a network structure and can usefully be represented as graphs. Network analysis focuses on the relations among the nodes exploring the properties of each network. We introduce a method for measuring the strength of the relationship between two nodes of a network and for their ranking. This method is applicable to all kinds of networks, including directed and weighted networks. The approach extracts dependency relations among the network’s nodes from the structure in local surroundings of individual nodes. For the tasks we deal with in this article, the key technical parameter is locality. Since only the surroundings of the examined nodes are used in computations, there is no need to analyze the entire network. This allows the application of our approach in the area of large-scale networks. We present several experiments using small networks as well as large-scale artificial and real world networks. The results of the experiments show high effectiveness due to the locality of our approach and also high quality node ranking comparable to PageRank.

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Efficient network immunization under limited knowledge

National Science Review ◽

10.1093/nsr/nwaa229 ◽

2020 ◽

Cited By ~ 1

Author(s):

Yangyang Liu ◽

Hillel Sanhedrai ◽

GaoGao Dong ◽

Louis M Shekhtman ◽

Fan Wang ◽

...

Keyword(s):

Real World ◽

Large Scale ◽

Complete Information ◽

Analytical Framework ◽

Epidemic Spreading ◽

Immunization Strategy ◽

Scale Free ◽

Limited Knowledge ◽

Small N ◽

Large Scale Networks

Abstract Targeted immunization of centralized nodes in large-scale networks has attracted significant attention. However, in real-world scenarios, knowledge and observations of the network may be limited, thereby precluding a full assessment of the optimal nodes to immunize (or quarantine) in order to avoid epidemic spreading such as that of the current coronavirus disease (COVID-19) epidemic. Here, we study a novel immunization strategy where only n nodes are observed at a time and the most central among these n nodes is immunized. This process can globally immunize a network. We find that even for small n (≈10) there is significant improvement in the immunization (quarantine), which is very close to the levels of immunization with full knowledge. We develop an analytical framework for our method and determine the critical percolation threshold pc and the size of the giant component P∞ for networks with arbitrary degree distributions P(k). In the limit of n → ∞ we recover prior work on targeted immunization, whereas for n = 1 we recover the known case of random immunization. Between these two extremes, we observe that, as n increases, pc increases quickly towards its optimal value under targeted immunization with complete information. In particular, we find a new general scaling relationship between |pc(∞) − pc(n)| and n as |pc(∞) − pc(n)| ∼ n−1exp(−αn). For scale-free (SF) networks, where P(k) ∼ k−γ, 2 < γ < 3, we find that pc has a transition from zero to nonzero when n increases from n = 1 to O(log N) (where N is the size of the network). Thus, for SF networks, having knowledge of ≈log N nodes and immunizing the most optimal among them can dramatically reduce epidemic spreading. We also demonstrate our limited knowledge immunization strategy on several real-world networks and confirm that in these real networks, pc increases significantly even for small n.

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