Unveiling Latent Structure of Venture Capital Syndication Networks
<p>Basic statistics of VC investment activities in China: (<b>a</b>) The number of investments and the number of startups got invested in each year; (<b>b</b>) The number of new VC institutions that enter the Chinese market each year.</p> "> Figure 2
<p>The illustration of our iterative Loubar method on classifying VC institutions: The partition based on (<b>a</b>) the number of investments, (<b>b</b>) the number of IPO and M&A. (<b>c</b>) the classification results are based on the number of investment deals and the number of IPO and M&A. The digit in the parentheses indicates the size of the category. The color of the symbols indicates the density of data points, a darker color corresponds to a higher density.</p> "> Figure 3
<p>Comparisons between VC institutions from different categories on the number of (<b>a</b>) industry, and (<b>b</b>) investment stages that they involved.</p> "> Figure 4
<p>Comparisons between VC institutions from different categories on (<b>a</b>) the success rate, which is measured by the fraction of invested startups that exit through IPO or M&A, and (<b>b</b>) the hawk eye index (HEI). Note that the first-tier category has a low median success rate but the highest median HEI, which indicates that they tend to invest more money on eventually successful startups out of a large number of alternative choices.</p> "> Figure 5
<p>Comparisons between VC institutions from five categories on the survival rate.</p> "> Figure 6
<p>Syndication probability <math display="inline"><semantics> <mrow> <msub> <mi>W</mi> <mrow> <mi>a</mi> <mi>b</mi> </mrow> </msub> <mo>/</mo> <msub> <mi>W</mi> <mi>a</mi> </msub> </mrow> </semantics></math> of VC institutions from different categories. The first-tier group and the fifth-tier group have the highest tendency to make joint-investment with VC institutions within the same category. Each row is subject to normalization, but each column is not subject to normalization.</p> "> Figure 7
<p>The difference between VC institutions of five categories identified by our iterative Loubar algorithm on three network centrality indicators: (<b>a</b>) degree; (<b>b</b>) closeness; and (<b>c</b>) k-core.</p> "> Figure 8
<p>The difference between VC institutions of five categories identified by the weighted k-means algorithm [<a href="#B24-entropy-24-01506" class="html-bibr">24</a>], which cannot rank obtained clusters, on three network centrality indicators: (<b>a</b>) degree; (<b>b</b>) closeness; and (<b>c</b>) k-core. Note the <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>,</mo> <mi>γ</mi> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> </mrow> </semantics></math> only denote different groups but not the rank.</p> "> Figure 9
<p>The two-dimensional projection of the cumulative syndication networks obtained by t-SNE algorithm in the year (<b>a</b>) 1998, (<b>b</b>) 2003, (<b>c</b>) 2008, and (<b>d</b>) 2011. Each node represents a VC institution with node color indicating the classification category obtained by our iterative Loubar method, and the gray line signifies the syndication relation between VC institutions.</p> "> Figure 10
<p>(<b>a</b>) The average number of VC institutions in the vicinity of a first-tier VC institution. The horizontal axis is the distance <span class="html-italic">R</span> in the embedded space and the vertical axis is the average number of VC institutions from different categories in the vicinity of a VC institution. The results are averaged for all VC institutions from the first-tier category. (<b>b</b>) The average fraction of VC institutions from different categories encountered in the vicinity with <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>1.35</mn> </mrow> </semantics></math> and (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>R</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> for VC institutions from different categories.</p> "> Figure A1
<p>Illustration of the criteria selection on the Lorenz curve of the Loubar method.</p> "> Figure A2
<p>Performing the iterative Loubar method on different distributions of data. (<b>a</b>) A power-law distribution with its exponent <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>2.65</mn> </mrow> </semantics></math>, which is displayed in a log-log fashion. (<b>b</b>) The illustration of the iterative Loubar method on the power-law distribution shown in (<b>a</b>). (<b>c</b>) The distribution of the classification results, which shows the number of categories and the number of enetities in each category, from the power-law distribution by the iterative Loubar method. (<b>d</b>–<b>f</b>) The same as (<b>a</b>–<b>c</b>) but on a normal distribution with mean equals 0.5 and standard deviation equals 0.1. (<b>g</b>–<b>i</b>) The same as (<b>a</b>–<b>c</b>) but on a delta distribution, where every entity is of the same value. (<b>j</b>–<b>l</b>) The same as (<b>a</b>–<b>c</b>) but on a uniform distribution, where all <span class="html-italic">n</span> entities have different values and equals 1 to <span class="html-italic">n</span>, respectively.</p> ">
Abstract
:1. Introduction
2. Data Preprocessing
3. Iterative Loubar Algorithm for Objective Classification
4. Investment Behaviors and Performance Analysis
5. Latent Structure of Joint-Investment Behaviors
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
VC | Venture Capital |
IPO | Initial Public Offering |
M&A | Merge and Acquisition |
ICNEAC | Industrial Classification for National Economic Activities of China |
HEI | Hawk Eye Index |
t-SNE | t-distributed Stochastic Neighbor Embedding |
Appendix A
Appendix A.1. Lorenz Curve
Appendix A.2. Loubar Algorithm
Appendix A.3. Iterative Loubar Classification Algorithm
Appendix A.4. Iterative Loubar Classification Performance for Different Types of Distributions
References
- Gompers, P.A.; Lerner, J. The Venture Capital Cycle; MIT Press: Cambridge, MA, USA, 2004. [Google Scholar]
- Wang, C.; Wang, L.; Xue, Y.; Li, R. Revealing spatial spillover effect in high-tech industry agglomeration from a high-skilled labor flow network perspective. J. Syst. Sci. Complex. 2022, 35, 849–859. [Google Scholar] [CrossRef]
- Zinser, S. The VC Landscape in China. The Diplomat. 2021. Available online: https://thediplomat.com/2021/01/the-global-reach-of-chinas-venture-capital/ (accessed on 10 October 2022).
- Li, R.; Lu, L.; Cui, T.; Gu, W.; Ma, S.; Xu, G.; Stanley, H.E. Assessing the Attraction of Cities on VentureCapital From a Scaling Law Perspective. IEEE Access 2021, 9, 48052–48063. [Google Scholar] [CrossRef]
- Li, R.; Dong, L.; Zhang, J.; Wang, X.; Wang, W.; Di, Z.; Stanley, H.E. Simple spatial scaling rules behind complex cities. Nat. Commun. 2017, 8, 1841. [Google Scholar] [CrossRef] [Green Version]
- Burt, R.S. Structural Holes: The Social Structure of Competition; Harvard University Press: Cambridge, MA, USA, 2009. [Google Scholar]
- Katila, R.; Rosenberger, J.D.; Eisenhardt, K.M. Swimming with sharks: Technology ventures, defense mechanisms and corporate relationships. Adm. Sci. Q. 2008, 53, 295–332. [Google Scholar] [CrossRef] [Green Version]
- Uzzi, B. The sources and consequences of embeddedness for the economic performance of organizations: The network effect. Am. Sociol. Rev. 1996, 674–698. [Google Scholar] [CrossRef]
- Podolny, J.M. Networks as the pipes and prisms of the market. Am. J. Sociol. 2001, 107, 33–60. [Google Scholar] [CrossRef]
- Manigart, S.; Wright, M.; Lockett, A.; Meuleman, M.; Landström, H.; Bruining, H.; Desbrieres, P.; Hommel, U. Why do European venture capital companies syndicate? Erim Rep. Ser. Ref. 2002. ERS–2002–98–ORG. [Google Scholar]
- Lerner, J. The syndication of venture capital investments. Financ. Manag. 1994, 23, 16–27. [Google Scholar] [CrossRef]
- Hochberg, Y.V.; Ljungqvist, A.; Lu, Y. Whom you know matters: Venture capital networks and investment performance. J. Financ. 2007, 62, 251–301. [Google Scholar] [CrossRef] [Green Version]
- Sorenson, O.; Stuart, T.E. Syndication networks and the spatial distribution of venture capital investments. Am. J. Sociol. 2001, 106, 1546–1588. [Google Scholar] [CrossRef]
- Luo, J.D.; Li, R.; Fan, F.; Tang, J. Repeated Cooperation Matters: An Analysis of Syndication in the Chinese VC Industry by ERGM. In Social Network Analysis; CRC Press: Boca Raton, FL, USA, 2017; pp. 177–194. [Google Scholar]
- Wu, J.; Luo, C.; Liu, L. A social network analysis on venture capital alliance’s exit from an emerging market. Complexity 2020, 2020, 4650160. [Google Scholar] [CrossRef]
- Alexy, O.T.; Block, J.H.; Sandner, P.; Ter Wal, A.L. Social capital of venture capitalists and start-up funding. Small Bus. Econ. 2012, 39, 835–851. [Google Scholar] [CrossRef] [Green Version]
- Dimov, D.; De Clercq, D. Venture capital investment strategy and portfolio failure rate: A longitudinal study. Entrep. Theory Pract. 2006, 30, 207–223. [Google Scholar] [CrossRef]
- Luo, J.D.; Rong, K.; Yang, K.; Guo, R.; Zou, Y. Syndication through social embeddedness: A comparison of foreign, private and state-owned venture capital (VC) firms. Asia Pac. J. Manag. 2019, 36, 499–527. [Google Scholar] [CrossRef]
- Gu, W.; Jar-Der, L.; Liu, J. Exploring small-world network with an elite-clique: Bringing embeddedness theory into the dynamic evolution of a venture capital network. Soc. Netw. 2019, 57, 70–81. [Google Scholar] [CrossRef] [Green Version]
- Tykvová, T. Who chooses whom? Syndication, skills and reputation. Rev. Financ. Econ. 2007, 16, 5–28. [Google Scholar] [CrossRef] [Green Version]
- Liu, Z.; Chen, Z. Venture Capital Networks and Investment Performance in C hina. Aust. Econ. Pap. 2014, 53, 97–111. [Google Scholar] [CrossRef] [Green Version]
- Batjargal, B. Comparative social capital: Networks of entrepreneurs and venture capitalists in China and Russia. Manag. Organ. Rev. 2007, 3, 397–419. [Google Scholar] [CrossRef] [Green Version]
- Huang, H.; Tang, J.; Liu, L.; Luo, J.D.; Fu, X. Analysis and prediction of triadic closure in online social networks. In Social Network Analysis; CRC Press: Boca Raton, FL, USA, 2017; pp. 105–136. [Google Scholar]
- Yang, H.; Luo, J.D.; Fan, Y.; Zhu, L. Using weighted k-means to identify Chinese leading venture capital firms incorporating with centrality measures. Inf. Process. Manag. 2020, 57, 102083. [Google Scholar] [CrossRef]
- Aral, S.; Walker, D. Identifying influential and susceptible members of social networks. Science 2012, 337, 337–341. [Google Scholar] [CrossRef] [Green Version]
- Li, Q.; Zhou, T.; Lü, L.; Chen, D. Identifying influential spreaders by weighted LeaderRank. Phys. A Stat. Mech. Its Appl. 2014, 404, 47–55. [Google Scholar] [CrossRef]
- Li, R.; Wang, W.; Di, Z. Effects of human dynamics on epidemic spreading in Côte d’Ivoire. Phys. A Stat. Mech. Its Appl. 2017, 467, 30–40. [Google Scholar] [CrossRef] [Green Version]
- Lü, L.; Chen, D.; Ren, X.L.; Zhang, Q.M.; Zhang, Y.C.; Zhou, T. Vital nodes identification in complex networks. Phys. Rep. 2016, 650, 1–63. [Google Scholar] [CrossRef] [Green Version]
- Li, R.; Wang, W.; Shu, P.; Yang, H.; Pan, L.; Cui, A.; Tang, M. Review of Threshold Theoretical Analysis about Epidemic Spreading Dynamics on Complex Networks. Complex Syst. Complex. Sci. 2016, 13, 1–39. [Google Scholar]
- Gu, W.; Gao, F.; Lou, X.; Zhang, J. Discovering latent node Information by graph attention network. Sci. Rep. 2021, 11, 6967. [Google Scholar] [CrossRef] [PubMed]
- McGrath, R.G. Falling forward: Real options reasoning and entrepreneurial failure. Acad. Manag. Rev. 1999, 24, 13–30. [Google Scholar] [CrossRef]
- Louail, T.; Lenormand, M.; Ros, O.G.C.; Picornell, M.; Herranz, R.; Frias-Martinez, E.; Ramasco, J.J.; Barthelemy, M. From mobile phone data to the spatial structure of cities. Sci. Rep. 2014, 4, 5276. [Google Scholar] [CrossRef] [Green Version]
- Bassolas, A.; Barbosa-Filho, H.; Dickinson, B.; Dotiwalla, X.; Eastham, P.; Gallotti, R.; Ghoshal, G.; Gipson, B.; Hazarie, S.A.; Kautz, H.; et al. Hierarchical organization of urban mobility and its connection with city livability. Nat. Commun. 2019, 10, 4817. [Google Scholar] [CrossRef] [Green Version]
- Gao, T.; Xu, Z.; Liu, C.; Yang, Y.; Shang, F.; Li, R. Quantifying relation between mobility patterns and socioeconomic status of dockless sharing-bike users. arXiv 2022, arXiv:2204.03894. [Google Scholar]
- Beach, C.M.; Kaliski, S.F. Lorenz curve inference with sample weights: An application to the distribution of unemployment experience. J. R. Stat. Soc. Ser. C (Appl. Stat.) 1986, 35, 38–45. [Google Scholar] [CrossRef]
- Grover, A.; Leskovec, J. node2vec: Scalable feature learning for networks. In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 13–17 August 2016; pp. 855–864. [Google Scholar]
- These Are the Top Venture Capital Companies in China (2021). Available online: https://welpmagazine.com/these-are-the-top-venture-capital-companies-in-china-2021 (accessed on 23 August 2022).
- Jain, A. These Are the Top Venture Capital Firms of 2020. Available online: https://www.entrepreneur.com/article/361514 (accessed on 23 August 2022).
- Lange, J.E.; Bygrave, W.; Nishimoto, S.; Roedel, J.; Stock, W. Smart money? The impact of having top venture capital investors and underwriters backing a venture. Ventur. Cap. Int. J. Entrep. Financ. 2001, 3, 309–326. [Google Scholar] [CrossRef]
- Govindarajan, V.; Srivastava, A. The scary truth about corporate survival. Harv. Bus. Rev. 2016, 12, 24–25. [Google Scholar]
- Bonaventura, M.; Ciotti, V.; Panzarasa, P.; Liverani, S.; Lacasa, L.; Latora, V. Predicting success in the worldwide start-up network. Sci. Rep. 2020, 10, 345. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Kitsak, M.; Gallos, L.K.; Havlin, S.; Liljeros, F.; Muchnik, L.; Stanley, H.E.; Makse, H.A. Identification of influential spreaders in complex networks. Nat. Phys. 2010, 6, 888–893. [Google Scholar] [CrossRef]
- Evans, T.S.; Chen, B. Linking the network centrality measures closeness and degree. Commun. Phys. 2022, 5, 1–11. [Google Scholar] [CrossRef]
- Lü, L.; Zhou, T.; Zhang, Q.M.; Stanley, H.E. The H-index of a network node and its relation to degree and coreness. Nat. Commun. 2016, 7, 10168. [Google Scholar] [CrossRef] [Green Version]
- Perozzi, B.; Al-Rfou, R.; Skiena, S. Deepwalk: Online learning of social representations. In Proceedings of the 20th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, New York, NY, USA, 24–27 August 2014; pp. 701–710. [Google Scholar]
- Mikolov, T.; Chen, K.; Corrado, G.; Dean, J. Efficient estimation of word representations in vector space. In Proceedings of the Workshop at ICLR, Scottsdale, AZ, USA, 2–4 May 2013. [Google Scholar]
- Gu, W.; Tandon, A.; Ahn, Y.Y.; Radicchi, F. Principled approach to the selection of the embedding dimension of networks. Nat. Commun. 2021, 12, 3772. [Google Scholar] [CrossRef]
- Van der Maaten, L.; Hinton, G. Visualizing data using t-SNE. J. Mach. Learn. Res. 2008, 9, 11. [Google Scholar]
- Damgaard, C.; Weiner, J. Describing inequality in plant size or fecundity. Ecology 2000, 81, 1139–1142. [Google Scholar] [CrossRef]
- Louf, R. Wandering in cities: A statistical physics approach to urban theory. arXiv 2015, arXiv:1511.08236. [Google Scholar]
- Shang, F.; Chen, B.; Expert, P.; Lü, L.; Yang, A.; Stanley, H.E.; Lambiotte, R.; Evans, T.; Li, R. Local dominance unveils clusters in networks. arXiv 2022, arXiv:2209.15497. [Google Scholar]
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Gu, W.; Yang, A.; Lu, L.; Li, R. Unveiling Latent Structure of Venture Capital Syndication Networks. Entropy 2022, 24, 1506. https://doi.org/10.3390/e24101506
Gu W, Yang A, Lu L, Li R. Unveiling Latent Structure of Venture Capital Syndication Networks. Entropy. 2022; 24(10):1506. https://doi.org/10.3390/e24101506
Chicago/Turabian StyleGu, Weiwei, Ao Yang, Lingyun Lu, and Ruiqi Li. 2022. "Unveiling Latent Structure of Venture Capital Syndication Networks" Entropy 24, no. 10: 1506. https://doi.org/10.3390/e24101506