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Clique detection with a given reliability

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Abstract

In this paper we propose a new notion of a clique reliability. The clique reliability is understood as the ratio of the number of statistically significant links in a clique to the number of edges of the clique. This notion relies on a recently proposed original technique for separating inferences about pairwise connections between vertices of a network into significant and admissible ones. In this paper, we propose an extension of this technique to the problem of clique detection. We propose a method of step-by-step construction of a clique with a given reliability. The results of constructing cliques with a given reliability using data on the returns of stocks included in the Dow Jones index are presented.

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Data Availability

The dataset generated during and/or analysed during the current study can be downloaded for free from open sources using list of tickers.

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Acknowledgements

The results of the Sections 2 - 4 of the article were prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE). The results of the Sections 5 - 7 of the article were obtained with the support of the RSF grant N 22-11-00073.

Author information

Author notes

  1. Alexander Koldanov, Petr Koldanov and Panos Pardalos equally contributed to this work.

Authors and Affiliations

  1. Laboratory of Algorithms and Technologies for Network Analysis, National Research University Higher School of Economics, 136 Rodionova Street, Nizhny Novgorod, 603093, Russia

    Dmitry Semenov, Alexander Koldanov, Petr Koldanov & Panos Pardalos

  2. Center for Applied Optimization, University of Florida, Gainesville, FL, USA

    Panos Pardalos

Authors
  1. Dmitry Semenov
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  2. Alexander Koldanov
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  3. Petr Koldanov
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  4. Panos Pardalos
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Corresponding author

Correspondence to Dmitry Semenov.

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Appendix

Appendix

List of tickers of Dow Jones index:

Index in graph

Ticker

Company Name

0

AXP

American Express Company

1

AMGN

Amgen Inc.

2

AAPL

Apple Inc.

3

BA

The Boeing Company

4

CAT

Caterpillar Inc.

5

CSCO

Cisco Systems, Inc.

6

CVX

Chevron Corporation

7

GS

The Goldman Sachs Group, Inc.

8

HD

The Home Depot, Inc.

9

HON

Honeywell International Inc.

10

IBM

International Business Machines Corporation

11

INTC

Intel Corporation

12

JNJ

Johnson & Johnson

13

KO

The Coca-Cola Company

14

JPM

JPMorgan Chase & Co.

15

MCD

McDonald’s Corporation

16

MMM

3M Company

17

MRK

Merck & Co., Inc.

18

MSFT

Microsoft Corporation

19

NKE

NIKE, Inc.

20

PG

The Procter & Gamble Company

21

TRV

The Travelers Companies, Inc.

22

UNH

UnitedHealth Group Incorporated

23

CRM

Salesforce.com, inc.

24

VZ

Verizon Communications Inc.

25

V

Visa Inc.

26

WBA

Walgreens Boots Alliance, Inc.

27

WMT

Walmart Inc.

28

DIS

The Walt Disney Company

29

DOW

Dow Inc.

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Semenov, D., Koldanov, A., Koldanov, P. et al. Clique detection with a given reliability. Ann Math Artif Intell (2024). https://doi.org/10.1007/s10472-024-09928-8

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  • DOI: https://doi.org/10.1007/s10472-024-09928-8

Keywords

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