Document (#32590)

Author

Simkin, M.V.
Roychowdhury, V.P.

Title

¬A mathematical theory of citing

Source

Journal of the American Society for Information Science and Technology. 58(2007) no.11, S.1661-1673

Year

2007

Abstract

Recently we proposed a model in which when a scientist writes a manuscript, he picks up several random papers, cites them, and also copies a fraction of their references. The model was stimulated by our finding that a majority of scientific citations are copied from the lists of references used in other papers. It accounted quantitatively for several properties of empirically observed distribution of citations; however, important features such as power-law distributions of citations to papers published during the same year and the fact that the average rate of citing decreases with aging of a paper were not accounted for by that model. Here, we propose a modified model: When a scientist writes a manuscript, he picks up several random recent papers, cites them, and also copies some of their references. The difference with the original model is the word recent. We solve the model using methods of the theory of branching processes, and find that it can explain the aforementioned features of citation distribution, which our original model could not account for. The model also can explain sleeping beauties in science; that is, papers that are little cited for a decade or so and later awaken and get many citations. Although much can be understood from purely random models, we find that to obtain a good quantitative agreement with empirical citation data, one must introduce Darwinian fitness parameter for the papers.

Theme

Informetrie

Similar documents (content)

1. González-Teruel, A.; Pérez-Pulido, M.: ¬The diffusion and influence of theoretical models of information behaviour : the case of Savolainen's ELIS model (2020) 0.20

   0.19662775 = sum of:
     0.19662775 = product of:
       0.70224196 = sum of:
         0.024220362 = weight(abstract_txt:citation in 5974) [ClassicSimilarity], result of:
           0.024220362 = score(doc=5974,freq=1.0), product of:
             0.09044562 = queryWeight, product of:
               1.0309244 = boost
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.017916605 = queryNorm
             0.2677892 = fieldWeight in 5974, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
         0.12406716 = weight(abstract_txt:citing in 5974) [ClassicSimilarity], result of:
           0.12406716 = score(doc=5974,freq=4.0), product of:
             0.16931094 = queryWeight, product of:
               1.410508 = boost
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.017916605 = queryNorm
             0.73277694 = fieldWeight in 5974, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
         0.2698639 = weight(abstract_txt:cites in 5974) [ClassicSimilarity], result of:
           0.2698639 = score(doc=5974,freq=6.0), product of:
             0.24830182 = queryWeight, product of:
               1.7081382 = boost
               8.113368 = idf(docFreq=35, maxDocs=44218)
               0.017916605 = queryNorm
             1.0868382 = fieldWeight in 5974, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               8.113368 = idf(docFreq=35, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
         0.013583294 = weight(abstract_txt:that in 5974) [ClassicSimilarity], result of:
           0.013583294 = score(doc=5974,freq=2.0), product of:
             0.07412247 = queryWeight, product of:
               1.7459911 = boost
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.017916605 = queryNorm
             0.18325473 = fieldWeight in 5974, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
         0.062789395 = weight(abstract_txt:citations in 5974) [ClassicSimilarity], result of:
           0.062789395 = score(doc=5974,freq=1.0), product of:
             0.21504764 = queryWeight, product of:
               2.2480989 = boost
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.017916605 = queryNorm
             0.291979 = fieldWeight in 5974, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
         0.09084889 = weight(abstract_txt:papers in 5974) [ClassicSimilarity], result of:
           0.09084889 = score(doc=5974,freq=1.0), product of:
             0.31491062 = queryWeight, product of:
               3.3318646 = boost
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.017916605 = queryNorm
             0.28849104 = fieldWeight in 5974, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
         0.1168689 = weight(abstract_txt:model in 5974) [ClassicSimilarity], result of:
           0.1168689 = score(doc=5974,freq=5.0), product of:
             0.23975247 = queryWeight, product of:
               3.356948 = boost
               3.986234 = idf(docFreq=2231, maxDocs=44218)
               0.017916605 = queryNorm
             0.4874565 = fieldWeight in 5974, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               3.986234 = idf(docFreq=2231, maxDocs=44218)
               0.0546875 = fieldNorm(doc=5974)
       0.28 = coord(7/25)
   

2. García, J.A.; Rodriguez-Sánchez, R.; Fdez-Valdivia, J.: Social impact of scholarly articles in a citation network (2015) 0.19

   0.18588795 = sum of:
     0.18588795 = product of:
       0.66388553 = sum of:
         0.07323549 = weight(abstract_txt:citation in 1621) [ClassicSimilarity], result of:
           0.07323549 = score(doc=1621,freq=7.0), product of:
             0.09044562 = queryWeight, product of:
               1.0309244 = boost
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.017916605 = queryNorm
             0.80971843 = fieldWeight in 1621, product of:
               2.6457512 = tf(freq=7.0), with freq of:
                 7.0 = termFreq=7.0
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
         0.053765554 = weight(abstract_txt:explain in 1621) [ClassicSimilarity], result of:
           0.053765554 = score(doc=1621,freq=1.0), product of:
             0.14080192 = queryWeight, product of:
               1.2862854 = boost
               6.1096387 = idf(docFreq=266, maxDocs=44218)
               0.017916605 = queryNorm
             0.38185242 = fieldWeight in 1621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.1096387 = idf(docFreq=266, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
         0.15852721 = weight(abstract_txt:citing in 1621) [ClassicSimilarity], result of:
           0.15852721 = score(doc=1621,freq=5.0), product of:
             0.16931094 = queryWeight, product of:
               1.410508 = boost
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.017916605 = queryNorm
             0.9363081 = fieldWeight in 1621, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
         0.033261377 = weight(abstract_txt:several in 1621) [ClassicSimilarity], result of:
           0.033261377 = score(doc=1621,freq=1.0), product of:
             0.1170208 = queryWeight, product of:
               1.4361844 = boost
               4.5477557 = idf(docFreq=1272, maxDocs=44218)
               0.017916605 = queryNorm
             0.28423473 = fieldWeight in 1621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               4.5477557 = idf(docFreq=1272, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
         0.01901265 = weight(abstract_txt:that in 1621) [ClassicSimilarity], result of:
           0.01901265 = score(doc=1621,freq=3.0), product of:
             0.07412247 = queryWeight, product of:
               1.7459911 = boost
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.017916605 = queryNorm
             0.2565032 = fieldWeight in 1621, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
         0.07175931 = weight(abstract_txt:citations in 1621) [ClassicSimilarity], result of:
           0.07175931 = score(doc=1621,freq=1.0), product of:
             0.21504764 = queryWeight, product of:
               2.2480989 = boost
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.017916605 = queryNorm
             0.33369032 = fieldWeight in 1621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
         0.25432393 = weight(abstract_txt:papers in 1621) [ClassicSimilarity], result of:
           0.25432393 = score(doc=1621,freq=6.0), product of:
             0.31491062 = queryWeight, product of:
               3.3318646 = boost
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.017916605 = queryNorm
             0.8076067 = fieldWeight in 1621, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.0625 = fieldNorm(doc=1621)
       0.28 = coord(7/25)
   

3. Baird, L.M.; Oppenheim, C.: Do citations matter? (1994) 0.18

   0.18444821 = sum of:
     0.18444821 = product of:
       0.6587436 = sum of:
         0.077369116 = weight(abstract_txt:citation in 6896) [ClassicSimilarity], result of:
           0.077369116 = score(doc=6896,freq=5.0), product of:
             0.09044562 = queryWeight, product of:
               1.0309244 = boost
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.017916605 = queryNorm
             0.8554213 = fieldWeight in 6896, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
         0.01734851 = weight(abstract_txt:also in 6896) [ClassicSimilarity], result of:
           0.01734851 = score(doc=6896,freq=1.0), product of:
             0.0653438 = queryWeight, product of:
               1.0732005 = boost
               3.3983476 = idf(docFreq=4017, maxDocs=44218)
               0.017916605 = queryNorm
             0.2654959 = fieldWeight in 6896, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.3983476 = idf(docFreq=4017, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
         0.12532675 = weight(abstract_txt:citing in 6896) [ClassicSimilarity], result of:
           0.12532675 = score(doc=6896,freq=2.0), product of:
             0.16931094 = queryWeight, product of:
               1.410508 = boost
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.017916605 = queryNorm
             0.7402165 = fieldWeight in 6896, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
         0.12701523 = weight(abstract_txt:scientist in 6896) [ClassicSimilarity], result of:
           0.12701523 = score(doc=6896,freq=1.0), product of:
             0.21523012 = queryWeight, product of:
               1.5903202 = boost
               7.5537524 = idf(docFreq=62, maxDocs=44218)
               0.017916605 = queryNorm
             0.5901369 = fieldWeight in 6896, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.5537524 = idf(docFreq=62, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
         0.15738782 = weight(abstract_txt:cites in 6896) [ClassicSimilarity], result of:
           0.15738782 = score(doc=6896,freq=1.0), product of:
             0.24830182 = queryWeight, product of:
               1.7081382 = boost
               8.113368 = idf(docFreq=35, maxDocs=44218)
               0.017916605 = queryNorm
             0.6338569 = fieldWeight in 6896, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.113368 = idf(docFreq=35, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
         0.0274424 = weight(abstract_txt:that in 6896) [ClassicSimilarity], result of:
           0.0274424 = score(doc=6896,freq=4.0), product of:
             0.07412247 = queryWeight, product of:
               1.7459911 = boost
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.017916605 = queryNorm
             0.3702305 = fieldWeight in 6896, product of:
               2.0 = tf(freq=4.0), with freq of:
                 4.0 = termFreq=4.0
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
         0.12685375 = weight(abstract_txt:citations in 6896) [ClassicSimilarity], result of:
           0.12685375 = score(doc=6896,freq=2.0), product of:
             0.21504764 = queryWeight, product of:
               2.2480989 = boost
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.017916605 = queryNorm
             0.5898867 = fieldWeight in 6896, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.078125 = fieldNorm(doc=6896)
       0.28 = coord(7/25)
   

4. Huang, S.; Qian, J.; Huang, Y.; Lu, W.; Bu, Y.; Yang, J.; Cheng, Q.: Disclosing the relationship between citation structure and future impact of a publication (2022) 0.18

   0.18010987 = sum of:
     0.18010987 = product of:
       0.5628434 = sum of:
         0.0678029 = weight(abstract_txt:citation in 621) [ClassicSimilarity], result of:
           0.0678029 = score(doc=621,freq=6.0), product of:
             0.09044562 = queryWeight, product of:
               1.0309244 = boost
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.017916605 = queryNorm
             0.7496537 = fieldWeight in 621, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.013878808 = weight(abstract_txt:also in 621) [ClassicSimilarity], result of:
           0.013878808 = score(doc=621,freq=1.0), product of:
             0.0653438 = queryWeight, product of:
               1.0732005 = boost
               3.3983476 = idf(docFreq=4017, maxDocs=44218)
               0.017916605 = queryNorm
             0.21239673 = fieldWeight in 621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.3983476 = idf(docFreq=4017, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.04132596 = weight(abstract_txt:distribution in 621) [ClassicSimilarity], result of:
           0.04132596 = score(doc=621,freq=1.0), product of:
             0.118146576 = queryWeight, product of:
               1.1782668 = boost
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.017916605 = queryNorm
             0.3497855 = fieldWeight in 621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.070895515 = weight(abstract_txt:citing in 621) [ClassicSimilarity], result of:
           0.070895515 = score(doc=621,freq=1.0), product of:
             0.16931094 = queryWeight, product of:
               1.410508 = boost
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.017916605 = queryNorm
             0.4187297 = fieldWeight in 621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               6.699675 = idf(docFreq=147, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.015523765 = weight(abstract_txt:that in 621) [ClassicSimilarity], result of:
           0.015523765 = score(doc=621,freq=2.0), product of:
             0.07412247 = queryWeight, product of:
               1.7459911 = boost
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.017916605 = queryNorm
             0.20943399 = fieldWeight in 621, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.18985729 = weight(abstract_txt:citations in 621) [ClassicSimilarity], result of:
           0.18985729 = score(doc=621,freq=7.0), product of:
             0.21504764 = queryWeight, product of:
               2.2480989 = boost
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.017916605 = queryNorm
             0.88286155 = fieldWeight in 621, product of:
               2.6457512 = tf(freq=7.0), with freq of:
                 7.0 = termFreq=7.0
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.103827305 = weight(abstract_txt:papers in 621) [ClassicSimilarity], result of:
           0.103827305 = score(doc=621,freq=1.0), product of:
             0.31491062 = queryWeight, product of:
               3.3318646 = boost
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.017916605 = queryNorm
             0.32970405 = fieldWeight in 621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
         0.05973184 = weight(abstract_txt:model in 621) [ClassicSimilarity], result of:
           0.05973184 = score(doc=621,freq=1.0), product of:
             0.23975247 = queryWeight, product of:
               3.356948 = boost
               3.986234 = idf(docFreq=2231, maxDocs=44218)
               0.017916605 = queryNorm
             0.24913962 = fieldWeight in 621, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.986234 = idf(docFreq=2231, maxDocs=44218)
               0.0625 = fieldNorm(doc=621)
       0.32 = coord(8/25)
   

5. Mingers, J.; Burrell, Q.L.: Modeling citation behavior in Management Science journals (2006) 0.17

   0.17309453 = sum of:
     0.17309453 = product of:
       0.61819476 = sum of:
         0.048932523 = weight(abstract_txt:citation in 994) [ClassicSimilarity], result of:
           0.048932523 = score(doc=994,freq=2.0), product of:
             0.09044562 = queryWeight, product of:
               1.0309244 = boost
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.017916605 = queryNorm
             0.5410159 = fieldWeight in 994, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               4.896717 = idf(docFreq=897, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
         0.01734851 = weight(abstract_txt:also in 994) [ClassicSimilarity], result of:
           0.01734851 = score(doc=994,freq=1.0), product of:
             0.0653438 = queryWeight, product of:
               1.0732005 = boost
               3.3983476 = idf(docFreq=4017, maxDocs=44218)
               0.017916605 = queryNorm
             0.2654959 = fieldWeight in 994, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               3.3983476 = idf(docFreq=4017, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
         0.073054664 = weight(abstract_txt:distribution in 994) [ClassicSimilarity], result of:
           0.073054664 = score(doc=994,freq=2.0), product of:
             0.118146576 = queryWeight, product of:
               1.1782668 = boost
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.017916605 = queryNorm
             0.61833924 = fieldWeight in 994, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               5.596568 = idf(docFreq=445, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
         0.023765815 = weight(abstract_txt:that in 994) [ClassicSimilarity], result of:
           0.023765815 = score(doc=994,freq=3.0), product of:
             0.07412247 = queryWeight, product of:
               1.7459911 = boost
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.017916605 = queryNorm
             0.320629 = fieldWeight in 994, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               2.3694751 = idf(docFreq=11241, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
         0.21971713 = weight(abstract_txt:citations in 994) [ClassicSimilarity], result of:
           0.21971713 = score(doc=994,freq=6.0), product of:
             0.21504764 = queryWeight, product of:
               2.2480989 = boost
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.017916605 = queryNorm
             1.0217137 = fieldWeight in 994, product of:
               2.4494898 = tf(freq=6.0), with freq of:
                 6.0 = termFreq=6.0
               5.339045 = idf(docFreq=576, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
         0.12978414 = weight(abstract_txt:papers in 994) [ClassicSimilarity], result of:
           0.12978414 = score(doc=994,freq=1.0), product of:
             0.31491062 = queryWeight, product of:
               3.3318646 = boost
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.017916605 = queryNorm
             0.41213006 = fieldWeight in 994, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.2752647 = idf(docFreq=614, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
         0.10559197 = weight(abstract_txt:model in 994) [ClassicSimilarity], result of:
           0.10559197 = score(doc=994,freq=2.0), product of:
             0.23975247 = queryWeight, product of:
               3.356948 = boost
               3.986234 = idf(docFreq=2231, maxDocs=44218)
               0.017916605 = queryNorm
             0.44042078 = fieldWeight in 994, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               3.986234 = idf(docFreq=2231, maxDocs=44218)
               0.078125 = fieldNorm(doc=994)
       0.28 = coord(7/25)