# Predicting the Evolution of Physics Research from a Complex Network Perspective

^{1}

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*Entropy*

**2019**,

*21*(12), 1152; https://doi.org/10.3390/e21121152 (registering DOI)

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. GEP Method

#### 2.2. Bibliographic Coupling Network and Co-Citation Network

#### 2.3. Community Detection and Validation

#### 2.4. Intimacy Indices

#### 2.5. GED Method

#### 2.6. Feature Ranking

## 3. Results

#### 3.1. Physics Research Evolution for 1981–2010

#### 3.2. Event Labeling

- Continuing: A research field is said to be continuing when the problems identified and solutions obtained from one year to another are of an incremental nature. It is likely to correspond to the repeated hypothesis testing picture of the progress of science proposed by Karl Popper [33]. Therefore, in the CN, this would appear as a group of papers that are repeatedly cited together year-by-year. In the BCN, this shows up as groups of articles from successive years sharing more or less the same reference list.
- Dissolving: A research field is thought to disappear in the following year if the problems are solved or abandoned, and no new significant work is done after this. For the CN, we will find a group of papers that are cited up to a given year, but receiving very few new citations afterwards. In the BCN, no new relevant papers are published in the field; hence, the reference chain terminates.
- Splitting: A research field splits in the following year, when the community of scientists who used to work on the same problems starts to form two or more sub-communities, which are more and more distant from one another. In terms of the CN, we will find a group of papers that are almost always cited together up till a given year, breaking up into smaller and disjoint groups of papers that are cited together in the next year. In the BCN, we will find the transition between new papers citing a group of older papers to new papers citing only a part of this reference group.
- Merging: Multiple research fields are considered to have merged in the following year when the previously disjoint communities of scientists found a mutual interest in each other’s field so that they solve the problems in their own domain using methods from another domain. In the CN, we find previously distinct groups of papers that are cited together by papers published after a given year. In the BCN, newly published papers will form a group commonly citing several previously disjoint groups of older papers.

#### 3.3. Future Events’ Prediction

#### 3.4. Predictive Feature Ranking

#### 3.5. Changes to the Betweenness Distributions Associated with Merging and Splitting Events in BCN

#### 3.5.1. **1999.01** + **1999.02** → **2000.03**

^{6}times and measured the quartiles of these samples. When we draw random samples from a TC, the 25th, 50th, and 75th percentiles depend on the size of the TC. There as more variability in these quartiles in smaller samples than in larger samples. Therefore, in the test for statistical significance, the observed quartile had to be tested against different null model quartiles for samples of different sizes. To do this, we drew samples with a range of sizes from the same set of betweenness and, for a given quartile (25%, 50%, or 75%), fit the minimum quartile value against the sample size to a cubic spline and the maximum quartile value against sample size to a different cubic spline. With these two cubic splines, we could then check whether the observed quartile value for a sample of size n was more than or less than the null model minimum or maximum using cubic spline interpolation. From the histograms shown in Figure 9a, we see that the betweenness quartiles of $1999.01a$ were statistically larger than random samples of the same size from 1999.01, at the level of p < 10

^{−6}, which means the papers in $1999.01a$ had significantly larger betweenness than other papers in 1999.01.

#### 3.5.2. **1999.01** → **2000.02** + **2000.03**

#### 3.5.3. **1999.11** + **1999.12** → **2000.15**

#### 3.5.4. **1999.04** → **2000.06** and **1999.13** → **2000.16**

## 4. Discussion and Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

PR | Physical Review |

PRA | Physical Review A |

PRB | Physical Review B |

PRC | Physical Review C |

PRD | Physical Review D |

PRE | Physical Review E |

PRL | Physical Review Letters |

RMP | Reviews of Modern Physics |

BCN | Bibliographic coupling network |

CN | Co-citation network |

GEP | Group evolution prediction |

GED | Group evolution discover |

SI | Supplementary Information |

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**Figure 2.**The process of building a bibliographical coupling network (BCN) and co-citation network (CN) from the citation bipartite network for a given period: year t. Both BCN and CN are undirected and weighted; the weights denote the number of shared citations (BCN) or co-citing papers (CN). Separate topical clusters are extracted for BCN (${C}_{1}$, ${C}_{2}$) and CN (${C}_{3}$, ${C}_{4}$). Nodes with numbers are papers from a given period being considered, and nodes with letters are their references.

**Figure 3.**Comparison of PACS homogeneity between real BCN TCs, which are between 1991 and 2000 and have more than 100 papers, and their corresponding random collections. The fraction of the largest subset of papers sharing at least one PACS number as a function of s for real communities in the BCN and random collections. For clarity, the error bars are not shown in the figures because they are smaller than the marker size.

**Figure 4.**The alluvial diagram of APSpapers from 1981 to 2010 for the BCNs. Each block in a column represents a TC, and the height of the block is proportional to the number of papers in the TC. For clarity reason, only TCs comprising more than 100 papers are shown. TCs in successive years are connected by streams whose widths at the left and right ends are proportional to the forward and backward intimacy indices. The colors inside a TC represent the relative contributions from different journals.

**Figure 5.**The prediction quality of classification results. The F-measure values for the imbalanced BCN (

**A**) and CN (

**B**) datasets, as well as the balanced BCN (

**C**) and CN (

**D**) datasets. The distribution of classes in the training sets is provided for each dataset:

**A1**,

**B1**,

**C1**,

**D1**, respectively. For the imbalanced datasets, the classifier focused on the dominating continuing event. Balancing the datasets increased the overall prediction quality by over 20%.

**Figure 6.**Feature ranking. The most frequently selected features in 1000 iterations for the BCN (

**A**) and CN (

**B**) datasets. The context based features (number of papers published in a given journal) turned out to be the most informative, followed by the microscopic structural measures, especially closeness, degree, and betweenness.

**Figure 7.**Part of the BCN adjacency matrix for two TCs (red boxes) that ultimately merged. (

**a**) No links between the two TCs at first. (

**b**) Few links between the two TCs. (

**c**) More links between the two TCs. (

**d**) Many links between the two TCs, leading to their identification as a single merged TC (big red box) by the Louvain method.

**Figure 8.**(

**a**) The adjacency matrix of the BCN associated with the TCs 1999.01 (top dense block) and 1999.02 (bottom dense block). (

**b**) The adjacency matrix of the BCN associated with the TCs 1999.11 (top dense block) and 1999.12 (bottom dense block).

**Figure 9.**The lower (top), median (middle), and top quartile (bottom) of the betweennesses in (

**a**) $1999.01a$, (

**b**) $1999.02a$, (

**c**) $1999.01b$, (

**d**) $1999.01b\alpha $, (

**e**) $1999.01b\beta $, (

**f**) $1999.01a\alpha $, (

**g**) $1999.01a\beta $, (

**h**) $1999.11a$, (

**i**) $1999.11b$, (

**j**) $1999.12a$, and (

**k**) $1999.12b$ shown as red vertical lines and 10

^{6}random samples of the same number of betweennesses from 1999.01 (

**a**,

**c**–

**g**), or 1999.02 (

**b**), or 1999.11 (

**h**,

**i**), or 1999.12 (

**j**,

**k**) shown as blue histograms.The x-axes are “quartile value”, and y-axes are “null model density”.

**Table 1.**The five evolution events from 1999 to 2000 in the BCN alluvial diagram Figure 4 that we will study quantitatively. The naming convention for TC is that four digits before ‘.’ is the year of TC, two digits after ‘.’ is the position of the TC in the diagram, starting with 00 for the bottom TC; the one just above bottom is 01, and so on. In the left panel, we highlight the related TCs.

TC in 1999 | Event | TC in 2000 |
---|---|---|

1999.01 | split | 2000.02, 2000.03 |

1999.01, 1999.02 | merge | 2000.03 |

1999.04 | continue | 2000.06 |

1999.11, 1999.12 | merge | 2000.15 |

1999.13 | continue | 2000.16 |

**Table 2.**The 25th, 50th, and 75th percentiles of the betweenness of 1849 papers in 1999.01, the 164 papers in $1999.01a$, the 17 papers in $1999.01a\alpha $, the 147 papers in $1999.01a\beta $, the 1685 papers in $1999.01b$, the 907 papers in $1999.01b\alpha $, the 778 papers in $1999.01b\beta $, the 344 papers in 1999.02, the 144 papers in $1999.02a$, the 200 papers in $1999.02b$, the 1014 papers in 1999.11, the 299 papers in $1999.11a$, the 715 papers in $1999.11b$, the 988 papers in 1999.12, the 347 papers in $1999.12a$, and the 641 papers in $1999.12b$.

Percentile | |||
---|---|---|---|

25 | 50 | 75 | |

1999.01 | 8.06 × 10^{−6} | 5.73 × 10^{−5} | 2.05 × 10^{−4} |

$1999.01a$ | 5.90 × 10^{−5} | 1.58 × 10^{−4} | 4.67 × 10^{−4} |

$1999.01a\alpha $ | 7.77 × 10^{−6} | 1.95 × 10^{−5} | 2.44 × 10^{−4} |

$1999.01a\beta $ | 5.29 × 10^{−6} | 4.96 × 10^{−5} | 2.48 × 10^{−4} |

$1999.01b$ | 6.22 × 10^{−6} | 5.04 × 10^{−5} | 1.88 × 10^{−4} |

$1999.01b\alpha $ | 8.59 × 10^{−6} | 6.00 × 10^{−5} | 2.14 × 10^{−4} |

$1999.01b\beta $ | 7.97 × 10^{−6} | 5.32 × 10^{−5} | 1.83 × 10^{−4} |

$1999.02$ | 2.47 × 10^{−6} | 5.54 × 10^{−5} | 2.13 × 10^{−4} |

$1999.02a$ | 3.08 × 10^{−5} | 1.13 × 10^{−4} | 3.17 × 10^{−4} |

$1999.02b$ | 2.14 × 10^{−7} | 1.44 × 10^{−5} | 1.60 × 10^{−4} |

1999.11 | 1.73 × 10^{−5} | 9.04 × 10^{−5} | 2.81 × 10^{−4} |

$1999.11a$ | 6.38 × 10^{−5} | 1.98 × 10^{−4} | 4.61 × 10^{−4} |

$1999.11b$ | 9.91 × 10^{−6} | 6.17 × 10^{−5} | 2.17 × 10^{−4} |

1999.12 | 6.56 × 10^{−6} | 4.54 × 10^{−5} | 1.62 × 10^{−4} |

$1999.12a$ | 2.74 × 10^{−5} | 9.08 × 10^{−5} | 2.33 × 10^{−4} |

$1999.12b$ | 2.52 × 10^{−6} | 2.69 × 10^{−5} | 1.20 × 10^{−4} |

**Table 3.**The distributions of the betweennesses of papers in 1999.04 and 1999.13 that share common references with the other TCs in 1999 (1999.00 to 1999.15). The four columns below 1999.04 and 1999.13 denote the following: the first column shows how many papers have common references with the other TCs, while the second, third, and fourth columns show the lower, median, and upper quartile values of betweennesses of these papers, respectively. For example, there are 25 papers in 1999.04 that share common references with papers in 1999.03, and the betweennesses of these papers have a lower quartile value of 1.6 × 10

^{−5}, a median value of 4.3 × 10

^{−4}, and an upper quartile value of 8.1 × 10

^{−4}. Similarly, there are 254 papers in 1999.13 that share common references with papers in 1999.10, and the betweennesses of these papers have a lower quartile value of 3.6 × 10

^{−5}, a median value of 8.8 × 10

^{−5}, and an upper quartile value of 2.7 × 10

^{−4}. The bottom row “b” represents 1999.04b and 1999.13b, respectively, which are papers in 1999.04 and 1999.13 that have no references in common with papers in other TCs. A betweenness value in red means that it is larger than the maximum of the corresponding quartile distribution of 10

^{6}random samples, and a betweenness value in blue denotes it is smaller than the minimum of the corresponding 10

^{6}random samples.

1999.04 | 1999.13 | |||||||
---|---|---|---|---|---|---|---|---|

Size | Percentile | Size | Percentile | |||||

25 | 50 | 75 | 25 | 50 | 75 | |||

1999.00 | 12 | 9.0 × 10^{−5} | 1.1 × 10^{−3} | 2.3 × 10^{−3} | 1 | - | - | 1.8 × 10^{−3} |

1999.01 | 56 | 1.6 × 10^{−4} | 4.2 × 10^{−4} | 1.0 × 10^{−3} | 6 | 2.0 × 10^{−4} | 4.9 × 10^{−4} | 6.5 × 10^{−4} |

1999.02 | 6 | 3.0 × 10^{−4} | 5.1 × 10^{−4} | 7.4 × 10^{−4} | 2 | 6.0 × 10^{−4} | - | 2.6 × 10^{−4} |

1999.03 | 25 | 1.6 × 10^{−5} | 4.3 × 10^{−4} | 8.1 × 10^{−4} | 0 | - | - | - |

1999.04 | - | - | - | - | 8 | 1.5 × 10^{−4} | 4.8 × 10^{−4} | 8.0 × 10^{−4} |

1999.05 | 179 | 4.9 × 10^{−5} | 1.7 × 10^{−4} | 4.5 × 10^{−4} | 4 | 2.2 × 10^{−4} | 4.3 × 10^{−4} | 6.5 × 10^{−4} |

1999.06 | 110 | 8.7 × 10^{−5} | 2.0 × 10^{−4} | 6.2 × 10^{−4} | 40 | 5.9 × 10^{−5} | 1.6 × 10^{−4} | 4.5 × 10^{−4} |

1999.07 | 29 | 1.7 × 10^{−4} | 5.6 × 10^{−4} | 1.2 × 10^{−3} | 44 | 1.4 × 10^{−4} | 3.1 × 10^{−4} | 5.5 × 10^{−4} |

1999.08 | 63 | 1.1 × 10^{−4} | 3.2 × 10^{−4} | 8.6 × 10^{−4} | 17 | 2.2 × 10^{−4} | 5.2 × 10^{−4} | 8.5 × 10^{−4} |

1999.09 | 49 | 7.8 × 10^{−5} | 2.6 × 10^{−4} | 8.0 × 10^{−4} | 99 | 8.0 × 10^{−5} | 2.5 × 10^{−4} | 4.8 × 10^{−4} |

1999.10 | 53 | 1.2 × 10^{−4} | 3.8 × 10^{−4} | 8.2 × 10^{−4} | 254 | 3.6 × 10^{−5} | 8.8 × 10^{−5} | 2.7 × 10^{−4} |

1999.11 | 89 | 1.0 × 10^{−4} | 3.2 × 10^{−4} | 9.2 × 10^{−4} | 71 | 1.4 × 10^{−4} | 3.4 × 10^{−4} | 5.7 × 10^{−4} |

1999.12 | 53 | 8.7 × 10^{−5} | 2.9 × 10^{−4} | 9.3 × 10^{−4} | 39 | 1.3 × 10^{−4} | 2.7 × 10^{−4} | 4.6 × 10^{−4} |

1999.13 | 9 | 1.3 × 10^{−4} | 4.2 × 10^{−4} | 1.1 × 10^{−3} | - | - | - | - |

1999.14 | 62 | 1.4 × 10^{−4} | 4.8 × 10^{−4} | 1.0 × 10^{−3} | 210 | 4.2 × 10^{−5} | 1.0 × 10^{−4} | 2.7 × 10^{−4} |

1999.15 | 17 | 1.8 × 10^{−4} | 3.6 × 10^{−4} | 9.7 × 10^{−4} | 176 | 5.1 × 10^{−5} | 1.3 × 10^{−4} | 3.1 × 10^{−4} |

b | 88 | 2.1 × 10^{−6} | 2.2 × 10^{−5} | 5.8 × 10^{−5} | 27 | 9.1 × 10^{−11} | 4.3 × 10^{−6} | 1.8 × 10^{−5} |

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## Share and Cite

**MDPI and ACS Style**

Liu, W.; Saganowski, S.; Kazienko, P.; Cheong, S.A.
Predicting the Evolution of Physics Research from a Complex Network Perspective. *Entropy* **2019**, *21*, 1152.
https://doi.org/10.3390/e21121152

**AMA Style**

Liu W, Saganowski S, Kazienko P, Cheong SA.
Predicting the Evolution of Physics Research from a Complex Network Perspective. *Entropy*. 2019; 21(12):1152.
https://doi.org/10.3390/e21121152

**Chicago/Turabian Style**

Liu, Wenyuan, Stanisław Saganowski, Przemysław Kazienko, and Siew Ann Cheong.
2019. "Predicting the Evolution of Physics Research from a Complex Network Perspective" *Entropy* 21, no. 12: 1152.
https://doi.org/10.3390/e21121152