重み付きモジュラーネットワークにおける検出閾値
Filippo Radicchi1, Filipi N Silva1, Alessandro Flammini1
1Indiana University, Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Bloomington, Indiana 47408, USA.
Physical review. E
|February 20, 2026
まとめ
ネットワークにおけるコミュニティ構造の検出は、ある混合閾値までは可能です。この閾値はノード次数とエッジ重み分布に依存し、重みのばらつきが大きいほど検出が困難になります。
背景:
- コミュニティ検出アルゴリズムは、ネットワーク内のノードグループを識別することを目的としています。
- 重み付き植え込みパーティションモデルは、コミュニティ検出手法を評価するための標準的なベンチマークです。
- スペクトルモジュラリティ最適化は、コミュニティ検出のための一般的な技術です。
結論:
- エッジ重みのばらつきは、コミュニティ構造の検出可能性に大きく影響します。
- エッジ重みがコミュニティ構造に関する情報を持たない場合、それらを組み込むことは有害です。
- この結果は、重み付きネットワークにおけるスペクトルモジュラリティ最適化の限界とパフォーマンスに関する洞察を提供します。
関連する概念動画
Expected Frequencies in Goodness-of-Fit Tests
7.0K
A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).
7.0K
Critical Region, Critical Values and Significance Level
12.0K
The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the...
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the...
12.0K
Types of Errors: Detection and Minimization
8.7K
Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or relative terms.
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
Absolute error in a measurement is the numerical difference from the true or central value. Relative error is the ratio between absolute error and the true or central value, expressed as a percentage.
Errors can be classified by source, magnitude, and sign. There are three types of errors: systematic, random, and gross.
Systematic or...
8.7K
Detection of Gross Error: The Q Test
7.1K
When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be eliminated from the data set to ensure an accurate representation of the measured value. In many cases, outliers arise from gross errors (or human errors) and do not accurately reflect the underlying phenomenon. In some cases, however, these apparent outliers reflect true phenomenological differences. In these cases, we can use statistical methods...
7.1K
Difference from Background: Limit of Detection
9.0K
The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...
The LOD indicates the presence or absence...
9.0K
Network Function of a Circuit
1.1K
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
1.1K

