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By drawing on large-scale online data we construct and analyze the time-varying worldwide network of professional relationships among start-ups. The nodes of this network represent companies, while the links model the flow of employees and the associated transfer of know-how across companies. We use network centrality measures to assess, at an early stage, the likelihood of the long-term positive performance of a start-up, showing that the start-up network has predictive power and provides valuable recommendations doubling the current state of the art performance of venture funds. Our network-based approach not only offers an effective alternative to the labour-intensive screening processes of venture capital firms, but can also enable entrepreneurs and policy-makers to conduct a more objective assessment of the long-term potentials of innovation ecosystems and to target interventions accordingly.
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Predicting success in the worldwide start-up network
Moreno Bonaventura1,2,, Valerio Ciotti1,2,, Pietro Panzarasa2
Silvia Liverani1,3, Lucas Lacasa1, Vito Latora1,3,4,5
1School of Mathematical Sciences, Queen Mary University of London,
Mile End Road, E14NS, London (UK)
2School of Business and Management, Queen Mary University of London,
Mile End Road, E14NS, London (UK).
3The Alan Turing Institute, The British Library NW12DB, London (UK)
4Dipartimento di Fisica e Astronomia, Universit`
a di Catania and INFN, 95123 Catania (Italy)
5Complexity Science Hub Vienna (CSHV), Vienna (Austria)
M.B. and V.C. contributed equally to this work.
By drawing on large-scale online data we construct and analyze the time-
varying worldwide network of professional relationships among start-ups. The
nodes of this network represent companies, while the links model the flow of
employees and the associated transfer of know-how across companies. We use
network centrality measures to assess, at an early stage, the likelihood of the
long-term positive performance of a start-up, showing that the start-up net-
work has predictive power and provides valuable recommendations doubling
the current state of the art performance of venture funds. Our network-based
approach not only offers an effective alternative to the labour-intensive screen-
ing processes of venture capital firms, but can also enable entrepreneurs and
policy-makers to conduct a more objective assessment of the long-term poten-
tials of innovation ecosystems and to target interventions accordingly.
Recent years have witnessed an unprecedented growth of interest in start-up companies. Policy-
1
arXiv:1904.08171v1 [physics.soc-ph] 17 Apr 2019
makers have been keen to sustain young entrepreneurs’ innovative efforts with a view to inject-
ing new driving forces into the economy and foster job creation and technological advance-
ments (1–4). Investors have been lured by the opportunity of disproportionally high returns
typically associated with radical new developments and technological discontinuities. Large
corporations have relied on various forms of external collaborations with newly established
firms to outsource innovation processes and stay abreast of technological breakthroughs (5).
Undoubtedly, knowledge-intensive ventures such as start-ups can have a large positive impact
on the economy and society. Yet they typically suffer from a liability of newness (6), and
cannot avoid the uncertainties and sunk costs resulting from disruptive product developments,
uncharted markets and rapidly changing technological regimes (7). For these reasons, their
long-term benefits are inherently difficult to predict, and their economic net present value can-
not be unambiguously assessed (8).
Indeed traditional models of business evaluation, based on historical trends of data (e.g., on
sales, production capacity, internal growth, and markets size) are mostly inapplicable to start-
ups, chiefly because their limited history does not provide sufficient data. Venture capitalists
and private investors often evaluate start-ups primarily based on the qualifications and dexterity
of the entrepreneurs, on their potential to create new markets or niches and to unleash the “gales
of creative destruction” (9). The process of screening and evaluating companies in their early
stages is therefore a subjective and labor-intensive task, and is inevitably fraught with biases
and uncertainty.
To overcoming these limitation, we propose a novel and data-driven framework for assessing
the long-term economic potential of newly established start-ups. Our study draws upon the con-
struction and analysis of the worldwide network of professional relationships among start-ups.
Such network provides the backbone and the channels through which knowledge can be gained,
transferred, shared, and recombined. For instance, skilled employees moving across firms in
2
search of novel opportunities can bring with them know-how on cutting-edge technologies,
advisors who gained experience in one firm can help identify the most effective strategies in
another, whilst well connected investors, lenders and board members can rely on the knowledge
gained in one firm to tap business and funding opportunities in another.
Previous work has investigated how knowledge transfer impacts upon the performance of start-
ups; yet information flows have been simply inferred mainly through data on patents (10),
interorganizational collaborations (11), co-location of firms and their proximity to universi-
ties (12). Other studies have analyzed social networks (e.g., inventor collaboration networks,
interlocking directorates) to unveil the microscopic level of interactions among individuals; yet
their scope has been limited mostly to specific industries or small geographic areas, and to a
fairly small observation period (11, 13, 14). Owing to lack of data, what still remains to be
studied is the global network underpinning knowledge exchange in the worldwide innovation
ecosystem. Equally, the competitive advantage of differential information-rich network po-
sitions and their role in opening up, expediting, or obstructing pathways to firms’ long-term
success have been left largely unexplored.
The world-wide network of start-ups. Here we study the complex time-varying network
(15,16) of interactions among all start-ups in the worldwide innovation ecosystem over a period
of 26 years (1990-2015). To this end, we collected all data on firms and people (i.e., founders,
employees, advisors, investors, and board members) available from the www.crunchbase.com
website. Drawing on the data, we first constructed a bipartite graph in which people are con-
nected to start-ups according to their professional role. We then obtained the projected one-
mode time-varying graph in which start-ups are the nodes and two companies are connected
when they share at least one individual that plays or has played a professional role in both com-
panies (see Supplementary Material (SM) for details). At the micro scale, employees working
3
Figure 1: The time-varying network of professional relationships among start-ups. (A)
Countries that, over time, joined the largest connected component (LCC) of the worldwide
start-up (WWS) network are highlighted in blue. (B) Evolution over time of the number of
firms and links in the WWS network. (C) Evolution over time of the fraction of nodes in the
LCC. (D) Evolution over time of the closeness centrality rank of five popular firms. (E) Airbnb’s
ego-centered network.
4
in a company can perceive the intrinsic value of new appealing opportunities and switch compa-
nies accordingly. This mobility creates an intel flow between companies, where those receiving
employees increase their fitness by capitalizing on the know-how the employee is bringing with
her. Such microscopic dynamics is thus captured and modelled by the creation of new edges at
the level of the network of start-ups. As a consequence, companies which are perceived at the
micro scale as appealing opportunities by mobile employees will likely boost their connectivity
and therefore will acquire a more central position in the overall time-varying network.
The resulting time-varying World Wide Start-up (WWS) network comprises 41,830 companies
distributed across 117 countries around the globe, and 135,099 links among them (see Fig S3
and S4 in the SM). Fig 1A highlights the countries in which start-ups have joined, over time,
the largest connected component of the network (15, 16). Fig 1B indicates that the number of
nodes and links in the WWS network has grown exponentially over the last 26 years. In the
same period, various communities of start-ups around the globe have joined together to form
the largest connected component including about 80% of the nodes of the network (Fig 1C).
Currently, an average of 4,74 “degrees of separation” between any two companies characterizes
the WWS network.
At the micro scale, Fig 1E shows a snapshot of the network of interactions between Airbnb
and other companies based on shared individuals. As an illustration, in 2013 Airbnb hired Mr
Thomas Arend (highlighted in the red square), who had previously acted as a senior product
manager in Google, as an international product leader in Twitter, and as a product manager in
Mozilla. As previously pointed out, the professional network thus reveals the potential flow
of knowledge between Airbnb and the three other companies in which Mr Arend had played a
role. Moreover, as new links were forged over time, the topological distances from Airbnb to
all other firms in the WWS network were reduced, which in turn enabled Airbnb to gain new
knowledge and tap business opportunities beyond its immediate local neighborhood.
5
The mechanistic interpretation of employees’ mobility inducing link creation discussed
above and illustrated in Fig 1E suggests that the potential exposure to knowledge of a start-
up in the WWS network, and its subsequent likelihood to excel in the future, should be well
captured by its network centrality over time. To test this hypothesis we have considered dif-
ferent measures of node centrality (32). For parsimony here we focus on the results obtained
by closeness centrality as it assesses the centrality of a node in the network from its average
distance from all the other nodes, although similar results has also been found by some other
centrality measures, such as betweenness or degree (see SM). In each month of the observation
period, we ranked companies according to their values of closeness centrality (i.e., top nodes
are firms with the highest closeness). Fig 1D is an example of the large variety of observed
trajectories as companies moved towards higher or lower ranks, i.e., they obtained a larger or
smaller proximity to all other companies in the network. Notice that Apple has always been in
the Top 10 firms over the entire period, while Microsoft exhibited an initial decline followed by
a constant rise towards the central region of the network. The trajectories of once upon a time
younger start-ups, such as Facebook, Airbnb, and Uber, are instead characterized by an abrupt
and swift move to the highest positions of the ranking soon after their foundation, possibly as a
result of the boost in activity that has characterized the venture capital industry in recent years.
Early-stage prediction of high performance. To investigate the interplay between the po-
sition of a given firm in the WWS network and its long-term economic performance, from
www.crunchbase.com we collected additional data on funding rounds, acquisitions, and initial
public offerings (IPOs). For each month t, we obtained the list of N(t)firms, ranked in terms
of closeness, that can be classified as “open deals” for investors, namely: (i) they have not yet
received funding; (ii) they have not yet been acquired; and (iii) they have not yet been listed in
the stock exchange market (see Fig S5 in SM). As an example, the company WhatsApp, which
6
ranked 1,060th in June 2009 in the full list, occupied the 15th position in the open-deals list
in the same month. Notice that, by assessing a firm’s network position prior to any financial
acquisition or IPO, our analysis is not subject to possible biases arising from the effects that the
capital market might have upon the firm’s expected performance. Furthermore, predicting the
long-term economic performance of firms in the open-deal list is arguably a challenging task,
as illustrated by the fact that the average success of venture funds early-stage investments in
similar open deals is only around 10-15% (see section S4.2 in SM). Over the range of 26 years
of the dataset, a total of 5305 different start-ups were identified as open-deals.
Our recommendation method is based on the hypothesis that start-ups with higher values of
closeness centrality at an early stage are more likely to show signs of positive long-term eco-
nomic performance. Accordingly, we counted the total number M(t)of firms inside the open-
deal list that, within a time window t= 7 years starting at month t, succeeded in securing
at least one of the following positive outcomes: (i) they took over one or more firms; (ii) they
were acquired by one or more firms; or (iii) they underwent an IPO. To assess the accuracy of
our recommendation method in early identifying successful companies, we checked how many
of the Top n= 20 companies in the closeness-based ranking of open-deals obtained a positive
outcome (see Fig S6 in SM).
Fig 2A reports the “success rate” S(blue curve) of the recommendation method, defined as
S(t) = m(t)/n, where m(t)is the number of firms with a positive outcome included in the Top
n= 20 firms, and Srand(t) = M(t)/N(t)(black curve) is the success rate expected in the case
of random ordering of companies, i.e. the expected success of a null model of random sam-
pling without replacement which complies with a hypergeometric distribution (see SM section
4 for details). The p-value in the top panel of Fig 2A measures the probability of obtaining, by
chance, a success rate larger than S(t), with low values of p(highlighted regions) indicating the
time periods where the prediction is statistically significant (p-value <0.05). From mid 2001
7
to mid 2004, the success rate of our recommendation method (blue curve) is remarkably larger
than the one based on random expectations (black curve), and the p-value is always smaller than
0.01. S(t)exhibits an exceptional peak of 50% in June 2003 (p-value = 0.0001). From 2004 to
2007, the blue curve decreases, reaching a local minimum at a time when a global financial cri-
sis was triggered by the US housing bubble. In this period (as well as during the collapse of the
dot-com bubble in 1999-2001), even though the success rate still exceeds random expectations,
the high p-values indicate that the predictions are not statistically significant. Finally, after mid
2007, the performance of the prediction increases, and it stabilizes around 35% (p-value = 0.01).
For completeness, Fig S7 in SM reports results based on different lengths of the recommenda-
tion list and on different time windows. The observed dependence of the performance of our
network-based recommendation method on the level of external financial market stress should
be studied in more depth.
In Fig 2B, we characterize the overall performance of the recommendation method over the
entire period of observation. Results indicate that about 30% of the firms appearing in the Top
20 in any month from 2000 to 2009 have indeed achieved a positive economic outcome within 7
years since the time of our recommendation. The black error bars indicate the expected success
rates and standard deviations in the case of random ordering of companies (p-values in this case
are all below 105). Interestingly, the random null model provides an expected success rate
which is indeed comparable to the actual performance that venture funds focusing on early-
stage start-ups reach through costly and labour-intensive screening processes (see section 4.2 in
SM for details), while the performance of our recommendation method is considerably superior.
We further checked the robustness of our methodology by replicating the analysis based on the
Top 50 and Top 100 (reported in Fig 2B), for two additional time windows t= 6 and t= 8
years (see Fig S8 in SM) and an alternative method of aggregation of the success rate across
the entire observation period (see Fig S9 in SM). We also controlled for different confounding
8
factors such as start-up size, geographical location or structural role of venture capital funds in
the start-up network, finding that our conclusions hold (see section 5 of the SM).
Finally, notice that the method presented here only provides a simple heuristic recommendation,
i.e. it does not quantify the probability of each start-up in the open-deal list to show economic
success in the future. In Section 6 of the SM we further studied this possibility by using a suite
of logistic regression methods to predict success of each and every start-up in the open-deal list.
We indeed found that a snapshot of the closeness centrality ranking of a given start-up could
predict its future economic outcome (F1 SCORE = 0.6), in qualitative agreement with findings
in Fig 2.
Implications. As lack of data and subjective biases inevitably impede a proper and rigorous
evaluation of risky and newly established innovative activities, our study has indicated that the
network of professional relationships among start-ups can unlock the long-term potential of
risky ventures whose economic net present value would otherwise be difficult to measure. Our
recommendation method can help stakeholders devise and fine-tune a number of effective strate-
gies, simply based on the underlying network. Employees, business consultants, board mem-
bers, bankers and lenders can identify the opportunities with the highest long-term economic
potential. Individual and institutional investors can discern financial deals and build appropriate
portfolios that most suit their investment preferences. Entrepreneurs can hone their networking
prowess and strategies for sustaining professional inter-firm partnering and securing a winning
streak over the long run. Finally, governmental bodies and policy-makers can concentrate their
attention and efforts on the economic activities and geographic areas with the most promising
value-generating potential (e.g., activities with the capacity of job creation, youth employment
and skill development, educational and technological enhancement) for both the national and
local communities. Sociological and economic research has vastly investigated the impact of
9
Figure 2: Closeness-based ranking of open-deals and predicting long-term success. (A) The
performance of our recommendation method in predicting companies’ success on a monthly
basis compared to the expected performance of a null model (random ordering of companies).
The top panel reports the probability (p-value) of obtaining, by chance, a success rate larger than
the one observed in the corresponding month. The gray-shaded region indicates the time periods
where the prediction is statistically significant (p-value <0.05). (B) The overall performance
of our method over the entire period of observation based on the Top 20,50 and 100 firms with
the highest closeness centrality. The black error bars indicate the expected success rates and
standard deviations in the case of random ordering of companies.
10
knowledge spillovers (18), involvement in inter-firm alliances (19) and network position (20)
on firms’ performance, innovation capacity, propensity to collaborate, and growth rates. Yet,
whether the centrality in the professional network of newly established knowledge-intensive
firms can help predict their long-term economic success has largely remained a moot question.
Our work is the first attempt to pave the way in this direction, and represents a contribution,
from a different angle, to the ongoing discussion on the science of success (21), complementing
recent findings in different fields such as science (22–24) and arts (25, 26).
Acknowledgements: LL acknowledges funding from EPSRC grant EP/P01660X/1. VL acknowledges
funding from EPSRC grant EP/N013492/1. Authors express their gratitude to StartupNetwork s.r.l for
providing data and computational infrastructure.
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Supplementary Materials include:
Supplementary section S1) Data set: additional details
Supplementary section S2) Construction of the World Wide Start-up (WWS) network
Supplementary section S3) Analysis of the WWS network
Supplementary section S4) Open-deals recommendation method
Supplementary section S5) Additional analysis
Supplementary section S6) From recommendation to prediction of start-up success: supervised
learning approaches
Supplementary Tables S1–S4
Supplementary figures Fig S3–S19
Supplementary References (27–37)
14
SUPPLEMENTARY MATERIAL
S1 Data set: additional details
Data were collected from the crunchbase.com Web API and were updated until December
2015. The data provided by the Crunchbase website are manually recorded and managed by
several contributors (e.g., incubators, venture funds, individuals) affiliated with the Crunchbase
platform. Moreover, the data are further enriched by Web crawlers that scrape the Web, on a
daily basis, in search for news about IPOs, acquisitions, and funding rounds. To date Crunch-
base is widely regarded as the world’s most comprehensive open data set about start-up com-
panies. It contains detailed information on organizations from all over the world and belonging
to four categories, namely companies, investors, schools, and groups. Among schools there are
383 universities, including top-tier institutions such as Stanford University, the Massachusetts
Institute of Technology (MIT), and many others. In addition to people’s business activity, the
data track information about their educational paths, and consequently their access to academic
knowledge.
The total number of organizations listed at the date of data collection amounted to 530,604.
However, a large number of entries contained very limited information, no profile pictures, and
no employees’ records. Accordingly, we needed to clean the data keeping only the organiza-
tions for which enough information was provided, and for which such information was reliable
(see Section S2 for more details). This finally limited the number of organizations to 41,830.
For this work, all these organizations were included in the construction of the network. Notice
however, that only organizations belonging to the category “companies” and, at the same time,
15
younger than two years, have been included in the recommendation list. For each organiza-
tion we extracted all the people included in the team (e.g., founders, advisors, board member,
employees, alumni) and additional information such as details on firms’ foundation dates, lo-
cations of the firms’ headquarters, founding rounds, acquisitions, and IPOs. Organizations and
people are uniquely identified by alphanumeric IDs. All data are time-stamped, and an accurate
reconstruction of historical events was made possible by the use of trust codes, i.e., numerical
codes provided by Crunchbase to indicate the reliability of a certain timestamp. The timestamps
indicate the dates of foundation, funding rounds, acquisitions, and IPOs, as well as the start and
the end times of job roles.
S2 Construction of the World Wide Start-up (WWS) network
We constructed a bipartite time-varying graph with N1= 41,830 nodes representing organi-
zations distributed across 117 countries around the globe, N2= 36,278 nodes representing
people, and K12 = 284,460 links between people and organizations. The graph is time-varying
because each node and each link have an associated timestamp, representing, respectively, the
time an organization was founded and the time a person was affiliated (and held a variety of
roles) with a given organization. Notice that in the construction of the time-varying graph we
retained only the timestamps whose trust code guarantees the reliability of the year and month.
Additionally, we cleaned the data by solving and removing inconsistencies such as an em-
ployee’s role starting at a date prior to the company’s foundation. In these cases, we retained
the most reliable information according to the trust code value. Inconsistencies were removed
by adopting a strong self-penalising data cleaning strategy. In particular, we did not make any
assumption on dates, nor did we attempt to infer timestamps. As a result, we do not retain in the
graph links whose timestamps cannot be determined in a reliable way. This approach to data
cleaning strengthens the validity of our results because it ensures that companies do not gain
16
higher positions in the closeness centrality rank score as a result of connections that were forged
at subsequent dates to those incorrectly or only partially reported in the data set. In this way we
avoid biases that could artificially inflate the success rate of the method, and accordingly our
results can safely be seen as conservative lower bounds.
We then projected the bipartite time-varying graph onto a one-mode graph in which two
companies are connected when they share at least one individual that plays or has played a
professional role in both companies. Such a graph comprises N1= 41,830 companies and
K= 135,099 links among them, and is here referred to as the World Wide Start-up (WWS)
network. The projected graph is time-varying like the original bipartite graph: a link between
any two companies is forged as soon as one individual with a professional role in one company
takes on a role in the other company. Since the creation of these links denote intel transfer
between companies, we realistically assume that such intel flow generates considerable know-
how for the nodes receiving new links. Once created, the links are then maintained, since the
know-how of a given company is not destroyed or removed.
Figure S3: Assortativity and degree distribution of the WWS network. (A) Average degree
of nearest neighbours knn for classes of nodes with degree kin the WWS. (B) The power-law
degree distribution of the WWS network. (C) Similar to panel (A), but where all venture capital
firms (see Section S5.5 for a list) have been removed.
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S3 Analysis of the WWS network
For completeness, we have calculated a variety of quantities for measuring the characteristics
of the structure of the WWS network. In particular, from 1990 to 2015, for every month, we
have computed the number of companies (nodes) and links, and examined the partition of the
WWS network into distinct connected components. A connected component of a network is a
subgraph in which any two nodes are connected to each other by at least one path [15, 16]. If
the network has more than one component, one can identify the largest connected component
(LCC), namely the component with the largest number of nodes. The countries highlighted in
blue in Fig 1A (main text) are those that have at least one start-up that is part of the LCC of
the WWS network. Fig 1C (main text) shows a rapid growth in the fraction of start-ups in the
LCC, thus highlighting the tendency that companies have to establish new connections with
one another and move toward the core of the network. Like many other real-world complex
networks, the WWS network is characterised by a rich topological structure, a small average
shortest path length (`= 4.74), and a high value of the average clustering coefficient, C=
0.6, as expected from the one-mode projection of a bipartite network [15, 16]. The value of
the average shortest path length is similar to the one obtained for an equivalent Erd¨
os-Renyi
random graphs (29) with the same number of nodes and edges (`random = 4.17). However, the
statistical features of the WWS differ from those characterising random graphs: the degree
distribution approaches a power-law with an exponent greater than 2(see Fig. S3, panel B), the
assortativity coefficient (28) is positive, namely γ= 0.11 (see Fig. S3, panel A) and this result
holds even if all venture capital firms are removed from the network (panel C). The clustering
coefficient is significantly larger than the one obtained for a corresponding random network,
Crand = 0.00013.
To offer a glimpse of the structure of the WWS network, in Fig. S4 we show the subgraph
18
obtained by using the k-core decomposition technique and including only the nodes that belongs
to the 10th shell. The k-core decomposition of a graph (30–32) is a technique that iteratively
deletes nodes starting from the most peripheral ones (i.e., nodes with degree equal to 1) and pro-
gressively unveil the most central and interconnected core of the network. Nodes are assigned
to a core value equal to kaccordingly to the k-core subgraph to which they belong.
Figure S4: Visualisation of the WWS network. Owing to visualisation constraints, only the
10th shell of the k-core decomposition is displayed in the image. The graph shown here includes
8% of the nodes and 31% of the links in the complete WWS network.
S4 Open-deals recommendation method
Our working hypothesis is that companies with a central position in the network have higher
exposure to knowledge and easier access to resources than companies with peripheral positions.
If this is the case, centrally positioned companies will be better equipped to compete and have
higher chances to survive, grow and flourish than peripheral ones. We have therefore used
network centrality measures [15, 16] that capture the structural centrality of a node in a graph,
with a view to identifying companies with a large long-term economic potential.
19
The concept of centrality and the related measures were first introduced in the context of
social network analysis (32). the centrality of a company we have computed, on a monthly
basis, its closeness centrality in the WWS network. Several other centrality measures have also
been considered, and the results are reported in Section S5. The closeness centrality quantifies
the importance of a node in the graph by measuring its mean distance from all other nodes. The
closeness centrality Ci(t)of a node i,i= 1,2, . . . , N(t)is defined as:
Ci(t) = N(t)1
Pjdij (t),(S1)
where N(t)is the number of nodes in the graph at time t, while dij (t)is the graph distance
between the two nodes iand j, measured as the number of links in the shortest path between
the two companies. To account for disconnected components we used the generalisation of
closeness centrality proposed in (33).
Our claim is that young start-ups with proportionally higher values of closeness centrality
will have a higher likelihood to become successful in later years. This can be readily translated
into several possible heuristics to provide recommendation for investing into a given start-up.
Among other possibilities, we have considered the following recommendation method. For
each month t, we ranked all the N(t)companies according to their values of closeness centrality
Ci(t), such that the top nodes are those with the highest closeness. From the ranked lists we
then removed the companies that can reasonably be regarded as irrelevant deals to investors, i.e.,
those companies that had already been acquired, had already been listed in a stock market, or
had received funding from other investors. The N(t)companies retained in the analysis belong
to the so-called open-deals ranked list at month t. Notice that, by definition, the open-deal
list considers newly-established start-ups. As a matter of fact, incubators such as 500 Startups,
Y Combinator,Techstars or Wayra indeed target early-stage companies, i.e. they make risky
investments on ideas and small teams without much of previous history. Their investment targets
20
are therefore similar to the ones captured by our the definition of ‘open-deal list’, and it is easy
to realize that predicting future positive outcomes of firms in such a set is more challenging than
predicting future positice outcomes of more established firms.
Fig S5 shows an example of the procedure adopted. The companies highlighted in grey are
those which, prior to December 2008, had not yet received funding, had not yet been acquired,
or had no yet been listed in any stock market. These companies thus could be seen as investment
opportunities at month t. Since we want to focus on early-stage companies, we also removed
any company that was more than two years old.
S4.1 Success rate in open-deals lists
Each open-deals list in month tcontains M(t)successful companies (0M(t)N(t)), i.e.,
those companies that have obtained, within a time window t= 6,7or 8years since month
t, a positive outcome. A positive outcome is here defined in terms of the occurrence of at
least one of the following events: (i) the company makes an acquisition; (ii) the company is
acquired; or (iii) the company undergoes an IPO. To each company in the open-deals list we
then assigned the value of a binary variable, namely 1if the company has achieved a positive
outcome within the chosen time windows t, or 0otherwise. Fig S6 shows an example of the
monthly open-deals lists, in which names are replaced by their associated binary values. Notice
that the higher the number of ones in the top regions of the rankings, the better the performance
of the recommendation method in predicting positive outcomes.
We focus on companies in the top positions of our open-deals recommendation list, and
we indicate by m(t)the number of companies in the Top 20 in month tthat have obtained a
positive outcome, i.e., the number of ones in the first n= 20 entries of the list. Notice that
the same procedure has been repeated for the Top 50 companies (n= 50) to check for the
robustness of results. The accuracy of the recommendation method is assessed by computing
21
Figure S5: Example of the construction of the open-deals ranked list. For each month of
the observation period, all companies in the network were ranked according to their values of
closeness centrality. Top-ranked nodes are those with the highest closeness centrality in the
WWS network in the corresponding month. Only those companies (highlighted in grey) that
had not yet received funding, had not yet been acquired, and had not yet been listed in the stock
exchange market, were retained in the open-deals ranked list.
Figure S6: Illustrative example of a monthly open-deals ranking. Companies’ names are
replaced by the values of their associated binary variable, with a value equal to 1indicating the
achievement of a positive outcome. The last line reports the success rate STop10(t)of companies
in the Top 10 of our recommendation list.
22
the success rate S(t)defined as the ratio m(t)/n. How does this compare to a null model
where network properties are not taken into account? If the open-deals lists were randomly
ordered, the expected number of successful companies mrand(t)in e.g. the Top 20 (n= 20)
would be given by the expected value of the hypergeometric distribution H(N(t), M(t), n). In
particular, the expected value of mrand(t)is nM (t)/N(t)and thus the expected success rate is
Srand(t) = M(t)/N(t). Similarly, it follows that var(Srand(t)) = var(mrand(t))/n2.
Fig 2 (main text) and Fig S7 show that S(t)(blue curve) is systematically much higher than
Srand(t)(black curve), except during two short periods corresponding, respectively, to the dot-
com bubble (1999-2001) and to the 2008 financial crisis. In both cases, the difference between
S(t)and Srand(t)becomes narrower, yet S(t)always remains higher than Srand(t). Moreover,
Fig S7 shows that these findings are robust against variations in the length of the time window
(i.e., t= 6,7,8) and in the number of companies considered in the recommendation (i.e., Top
20 and Top 50).
The statistical significance of the results is assessed by computing the hypergeometric p-
values, which give the probability of obtaining, by chance, a success rate equal to or greater
than the one obtained with real data. Denoting as P(·)the probability mass function of mrand(t)
we can compute the p-value at time tas:
p(t) =
n
X
k=m(t)
P(mrand(t) = k).
The top charts in Fig 2 (main text) and in each panel of Fig S7 report the evolution of the p-
values over time. Low p-values (<0.05) are observed in most parts of the observation period.
This suggests that the discrepancy between the success rate of the 20 top-ranked companies
selected according to our recommendation method and the success rate of the same number of
companies selected at random from the open-deals list is statistically significant. Conversely,
high p-values are observed in correspondence of the downturns, thus indicating that in such
23
periods the success rates predicted by our recommendation method could have been obtained
also by chance.
S4.2 Real investors performance is similar to random expectation
It is important to highlight that, although the random expectation null model has mainly been
introduced to assess whether our results are statistically significant, the performance of real
investements is remarkably similar to the expected success rate in the null model. To illustrate
this, a summary statistics of the Top 15 investors, according to the number of investments, is
reported in Table S4.2 (data extracted from crunchbase.com). Notice that there is a great
variability in investors performance, which reflects the variability in the type of investments.
Highlighted in pink are those investors whose target complies with our definition of open-deal
list. Incubators such as 500 Startups,Y Combinator,Techstars or Wayra focus indeed their
interest on very early-stage companies, i.e. they invest on ideas and small teams of entrepreneurs
without much history. They make the most risky bets in the landscape of start-ups investments
and their performance lies around 15%. Their investment target is very close to the type of
companies that we have isolated in our definition of “open deals”. On the other end, large
venture firms such as Intel Capital,Accel Partners, or Goldman Sachs invest in companies
at later stage of maturity. They are interested in organizations with larger teams, that have
already previously received funding, and they typically inject funds to boost a business that
has already found a market fit and has history of revenues, customers, and other indicators of
growth. The presence of quantitative indicators of growth allows large venture firms to perform
a more objective evaluation of the company and its success potential, which in turn is reflected
on higher investment performances.
In summary, while investors decide on which start-ups to invest through costly and labour-
intensive screening processes, results confirm that the percentage of real investments that were
24
Figure S7: The success rate of our recommendation method. The success rate S(t)of
our method (blue curve) is compared to the expected success rate Srand(t)associated with
the recommendation of randomly selected companies (black curve). Different lengths, namely
n= 20,50, of the recommendation lists, and different time windows, i.e., t= 6,7,8years, to
assess the performance of a company have been considered. The statistical significance of the
discrepancy between S(t)and Srand(t)is quantified through the associated p-values, shown in
the top charts of each panel.
25
Investor # investments # successful investments Success rate
500 Startups 1022 153 15%
Y Combinator 953 154 16%
Intel Capital 744 313 40%
Start-up Chile 710 10 1.4%
Sequoia Capital 700 267 38%
New Enterprise Associates (NEA) 672 272 40%
SV Angel 600 258 43%
Techstars 549 95 17%
Brand Capital 537 80 14%
Accel Partners (Accel) 536 270 50%
Sos Ventures (SOSV) 493 17 3%
Wayra 476 11 2%
Kleiner Perkins Caufield & Byers (KPCB) 457 203 43%
Right Side Capital Management (RSCM) 449 44 10%
Goldman Sachs 410 209 50%
Table S1: Top 15 investment companies according to the number of investments made, along
with the percentage of successful investments. Highlighted in pink are investors focused on
very early-stage companies as those considered in our open-deal lists. The success rates of such
investors are comparable to the random expectation null model, and much below the success
rate obtained using our recommendation method.
deemed ‘successful’ is consistently similar to the success rate given by our random expectation
model. In other words, state-of-the-art success rate is not much better than a random expectation
null model. This means that any improvement upon the null model provides valuable informa-
tion. We conclude that our recommendation method based on centrality –whose success rate
consistently exceeds random expectation over several periods– is a considerable improvement
with respect to the state of the art.
S4.3 Details on overall success rate
To obtain an overall measure of the performance of our method, the success rate can be aggre-
gated across the entire observation period. This can be carried out in two complementary ways
leading to two different measures of the overall success, namely e
SIand e
SII. Here we discuss
and provide some details with regards to both measures.
26
The first measure of overall success rate, e
SI, which is used in the main text, takes into
account the total number of positive entries in the top positions in all open-deals lists, regardless
of the specific companies that occupy those positions. In this way e
SIprovides a measure of the
overall goodness of the ranking across months, but it does not provide information about the
number of unique companies correctly or wrongly identified as successful. As an example of the
computation of e
SI, let us consider the period starting in January 2000 and ending in December
2007, and the Top 20 companies (bottom-left charts in Fig S7). Such a period includes δ= 96
months. The overall success rate e
SIis defined as:
e
SI=emI
enI
,
where enI= 20 δis the total number of entries in the Top 20 list across the δmonths, and
emI=Ptm(t), where the sum runs over all months in the observation period. To construct a
null model to which we can compare these measures, we then proceed to randomly shuffling
the entries in each open-deal list independently for each month and apply the same procedure
(i.e., the null model makes a random sampling of the list without replacement). Accordingly, at
month twe count the number of successful companies within the Top 20 and label it mrand(t).
The expected total number of successful companies within all the Top 20 lists in this null model
is thus given by:
emrand
I=X
t
mrand(t),
and the corresponding variance is given by the sum of the variances in each month
var(emrand
I) = X
t
var(mrand(t)),
where var(mrand(t)) denotes the variance associated to the random null model, i.e. the variance
of the hypergeometric distribution. The expected overall success rate in the case of random
ordering is then given by
e
Srand
I=emrand
I
enI
,
27
Figure S8: Observed and randomly expected success rates. The overall success rate em-
pirically found e
SI(blue bars), the overall success rate e
Srand
Iexpected by chance (black dots),
and its standard deviation (black error bars), for various values of tand lengths of the list of
top-ranked companies (i.e., Top 20, 50, and 100).
and its standard deviation σIis
σI=pvar(emrand
I)
enI
.
Figure S8 reports the overall success rate empirically found e
SI(blue bars), the overall success
rate e
Srand
Iexpected by chance (black dots), and its standard deviation (black error bars) for
various values of t, and for different numbers of recommended companies (i.e., Top 20, 50,
and 100).
The second measure of the overall success rate, e
SII, does not simply capture the overall
28
performance of the ranking-based recommendation method, but compares the number of unique
companies in the Top 20s correctly predicted as successful by our method, across the entire
observed period, against the number of successful companies that would be expected under
random selection. In particular, this second measure of overall success is based on: (i) the total
number e
NII of unique companies available in any month; (ii) the total number f
MII of unique
companies that have achieved a positive outcome at any time since their foundation up to 2015;
(iii) the number enII of unique companies included in all Top 20 rankings in any month; and (iv)
the number emII of unique companies, listed in all Top 20 rankings, that have achieved a positive
outcome at any time since their foundation up to 2015.
Notice that, in this way, each company contributes only once to the evaluation of the success
rate. Therefore, the probability of finding exactly emII successful companies in any ranking of
Top 20 (50, or 100) is given by the hypergeometric function H( e
NII,f
MII,enII ,emII). The success
rate shown in Fig S9 is computed as e
SII =emII/enII , while the success rate e
Srand
II in the case of
the null model is given by e
Srand
II = (f
MII/e
NII). Fig S9 reports also the error bars of the success
rate computed as the standard deviation of the hypergeometric distribution.
While the first index of overall performance assesses the average goodness of the ranking,
the second index measures only the number of companies correctly identified as successful
across the entire observation period. The two aggregation methods produce comparable results,
and achieve a substantial success rate of about 40% in the case of t=. Moreover, in
both cases, the success rate found in reality and the one expected by random chance are very
different, and their discrepancy is always statistically significant with p-values smaller than
105.
29
Figure S9: Observed and randomly expected success rates. The overall success rate e
SII (blue
bars) obtained through the second method of aggregation assessed against the overall success
rate e
Srand
II expected by chance (black dots), and its standard deviation (black error bars), for
various lengths of the list of top-ranked companies (i.e., Top 20, 50, and 100).
S5 Additional analysis
S5.1 Closeness centrality in successful vs non-successful start-ups
To have a better understanding of how closeness centrality is distributed among start-ups, in Fig
S10 we compare the estimated frequency histograms of closeness centralities rescaled ranking.
To obtain the rescaled ranking, in each calendar month we calculated the closeness centrality
of each firm in the global network and ranked all firms in terms of their centrality, what gives
an ‘absolute rank‘ for each firm. We then extract those firms which belong to the open-deal
list, and re-rank them accordingly (so that the firm with top ranking acquires a rank 0in the
open-deal ranking, the second acquires rank 1, and so on). The rescaled ranking is then defined
as the ratio between the open-deal-rank and the maximum absolute-rank of open-deal compa-
nies at a given month. Thus, the firm with the highest position (i.e., zero ranking) maintained
the same value (i.e., zero) in the rescaled ranking. By contrast, firms at lower positions were
30
Figure S10: Closeness centrality distributions. Histograms of closeness centrality rescaled
rankings (in bins of 0.005, see the text) for start-ups which will have a positive outcome (blue)
and for which no positive outcome occurs (orange). Successful start-ups have statistically lower
rescaled rankings (i.e. higher centralities) than non-successful ones. For every start-up, only
the value of closeness centrality collected in the last month of observation has been used.
assigned rescaled values approaching 1 as their ranking approached the highest value (i.e., the
lowest position). Such a rescaling thus enables to appropriately compare firms characterised by
different values of centrality, obtained in different networks and at different calendar times. In
order to smooth out the data, a binning has been performed in the x axis (bin size of 0.005). We
notice that histograms are non-overlapping, and that there is a net overabundance of start-ups
with a positive outcome (successful) closer to the top of the ranking. In other words, start-ups
which are higher in the centrality rankings (i.e. small values of closeness centrality ranks) have
statistically a higher chance of positive economic outcomes. This confirms that rankings based
on closeness centrality are indeed informative of a start-up long-term success and can then be
used to inform recommendation.
31
S5.2 Different centrality measures are correlated
We have considered closeness centrality as our primary measure of network centrality. Close-
ness centrality is based on the lengths of shortest paths in the network. However, the structural
centrality of a node in a network can be quantified by different network metrics, either global
such as closeness and betweenness, and local as the degree centrality (32). Closeness centrality
of a node (Eq.S1) characterises the overall distance between that node and the rest of the nodes
in the network, such that the lower that overall distance, the higher this measure, and hence the
more central this node is.
On the other hand, the betweenness centrality bi(t)of a node iwhen the network is observed at
a given time tis given by
bi(t) = 1
(N1)(N2)
N
X
j=1,j6=i
N
X
k=1,k6=i,j
njk (i;t)
njk (t),(S2)
where njk (t)is the total number of shortest paths between nodes jand kwhereas njk (i)is
the number of shortest paths between jand kthat actually go through i. This measure was
introduced by Freeman to quantify the fact that communication travels just along shortest paths,
and so a node iis more ‘central’ the more shortest paths among pairs of nodes in the network
go through it.
While both closeness and betweenness are measures of centrality based on shortest paths, one
can also think of a node being central if it acquires many edges over time –i.e. acquiring intel
from several other companies–. To account for this we may resort to use (normalised) degree
centrality d(i), defined as
di(t) = ki(t)
kmax(t),(S3)
where ki(t)is the degree (number of links) of node iand kmax(t)is the largest degree in the
network at that particular time snapshot.
32
Consequently, the centrality of a start-up in the WWS network can be measured in many
alternative ways. In this section we will show that the choice of using closeness centrality is not
only supported by theoretical arguments based on employees’ mobility and intel flows among
companies, but it also a robust choice as other alternative measures produce similar results.
To validate robustness, for each start-up in the open-deal list across time we have computed
additional centrality measures, namely degree and betweeness centrality (27), and computed
to which extent all three possible measures of centrality are correlated. More concretely, we
consider all start-ups in the open-deal list for which (i) we have data of the three centralities
over at least 3 of the 24 months forming the observation window, and for which (ii) closeness
and betweeness centralities are defined. For each firm, we then compute the Pearson correlation
coefficient between the monthly sequence of each pair of (rescaled) centrality measures. We
do this for all firms and we then construct the frequency histogram of the Pearson correlation
coefficients. Results are reported in Fig. S11. Interestingly, we find that the three measures are
in general well (pairwise) correlated. We conclude that the choice of a particular type of global
centrality measure, such as closenness, is a robust choice as other global structural indicators
based on a different use of shortest paths and, to a minor extent, also local measures such as
the degree are correlated with the closeness in the case of the WWS network under analysis in
this work. Hence, focusing on closeness centrality is a robust choice. In the next subsection
we round-off this validation by exploring results of our recommendation method using either
betweenness or degree centrality as the key network indicator, and will show that success rates
of the recommendation method are similar in all three cases.
S5.3 Recommendation methods based on other centrality measures
To further complement the correlation analysis of the previous subsection, here we focus on
recommendation methods based on centrality measures other than closeness. Results are sum-
33
(a)
Correlations CB
Density
−1.0 −0.5 0.0 0.5 1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
(b)
Correlations BD
Density
−1.0 −0.5 0.0 0.5 1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
(c)
Correlations CD
Density
−1.0 −0.5 0.0 0.5 1.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Figure S11: Centrality measures are correlated. Frequency histograms of the Pearson
correlation coefficients between (a) rescaled closeness and rescaled betweeness centrality, (b)
rescaled betweeness and rescaled degree centrality, and (c) rescaled closeness and rescaled de-
gree centrality. We find that centrality measures are systematically correlated between each
other, so the choice of using closeness centrality as the centrality measure under analysis is
robust.
marised in Fig.S12 for averages over the entire period, and in Figs.S13 and S14 for monthly
analysis. In every case we find that the results are qualitatively similar whether we use closeness,
betweeness or degree centrality, with success rates systematically larger than random expecta-
tions (and therefore larger than the actual perfomance of accelerators and investors focusing on
early-stage start-ups).
S5.4 The effect of fading links
The mobility of workers from one company to another creates an intel flow between compa-
nies. Our working hypothesis is that companies receiving employees increase their fitness by
capitalising on the know-how the employee is bringing with him/her. Such microscopic dynam-
ics is thus captured and modelled by the creation of new edges at the level of the network of
start-ups. As a consequence, companies which are perceived at the micro scale as appealing op-
34
Figure S12: Overall success rate of recommendation methods based on different centrality
measures. Comparison of recommendation methods focusing on the top 20, top 50 and Top
100 rankings, for t= 5,6,7and years, using different centrality measures. Closeness,
degree and betweeness centralities perform similarly, and recommendations based on either of
these measures are systematically superior to a random expectation model, with overall success
rates which are systematically larger than in the null model.
35
Figure S13: Monthly success rate of recommendation methods based on betweeness cen-
trality. Recommendation methods focusing on the Top 20 and Top 50 ranked start-ups in the
open-deal list, for t= 5,6,7and years, using betweeness centrality instead of closeness
centrality. Results are qualitatively similar and the monthly success rate of recommendations
based on betweenness is systematically superior to that of a random expectation model.
36
Figure S14: Monthly success rate of recommendation methods based on degree centrality.
Recommendation methods focusing on the Top 20 and Top 50 ranked start-ups in the open-
deal list, for t= 5,6,7and years, using degree centrality instead of closeness centrality.
Results are qualitatively similar and the monthly success rate of recommendations based on
degree centrality is systematically superior to that of a random expectation model.
37
portunities by mobile employees will likely boost their connectivity and therefore will acquire
a more central position in the WWS network. An important underlying assumption is that, once
a link is created, it will remain in the network indefinitely, so that the company that has received
the intel keeps it and builds on this intel forever. Conversely, considering the possibility of re-
moving links (or actually fading their strength) some time after their creation, would actually
be equivalent to assume that companies can lose the know-how they have acquired, something
which is less likely to occur. Accordingly, allowing links to fade or be removed with time in the
construction of the time-varying WWS network should lead to recommendations on the positive
economic outcome with much lower success rates than those obtained from a network where
know-how is not artificially removed. To check for this case, we have first build the WWS (for
each month) from January 1990 to December 1999. Then, starting from January 2000 onwards,
for each month all connections older than 10 years are removed from the network. Closeness is
then evaluated each month as described in the recommendation method. A similar analysis is
also performed for 5-year fading instead of 10-year fading, with very similar results.
In Fig.S15 we compare the overall success rate for the 5-year fading case (red bars) to our
standard recommendation method based on a WWS network that does not allow link fading.
Results show that a recommendation method with fading links systematically fails. In fact
it works even worse than a random null model, in good logical agreement with our previous
discussion. For completeness, a comparison of the two methods is also considered for the
monthly success rates in Fig.S16. Results are consistent with those obtained for the overall
success rate.
All these results strengthen our working hypothesis that the intel flow across start-ups is
well captured by node centrality in the WWS network.
38
Figure S15: Effects of fading links and removal of venture capital funds. Success rate of
recommendation methods focusing on the Top 20, Top 50 and Top 100 rankings, for t=
5,6,7and years. The standard case of closeness centrality from the original network (blue
bars) is compared to closeness centrality in a case where the links of the WWS are allowed
to fade over time (red bars), and to closeness centrality in a situation where all venture capital
funds (VC) have been removed from the WWS network (green bars). Results from the null
model are plotted in black bars.
39
Figure S16: Effect of fading links on monthly success rates. Systematic comparison of the
monthly success rate of a recommendation based on the closeness centrality from the original
network and in a case where the links of the WWS are allowed to fade over time. In the latter
case success rates drop below the random null model.
40
Figure S17: Comparison of monthly success rate of recommendation method based on a
worldwide start-up network with and without venture capital funds. Monthly success
rate of the recommendation method focusing in the Top 20 and Top 50, for t= 5,6,7and
years, comparing the original case to the case where all venture capital funds have been removed
from the worldwide start-up network. Results are essentially identical to the ones obtained in
the original case, hence confirming that the topological presence of venture capital funds is not
a confounding factor.
41
S5.5 Possible confounding factor 1: the effect of venture capital funds
A first possible confounding factor is the presence of venture capital funds, i.e. the fact that the
presence of these nodes in the network might enhance the closeness centrality of start-ups. In
order to assess the role played by venture capital funds in the effective centrality of different
start-ups, we have performed an experiment where we remove all venture capital funds from
the world start-up network, and subsequently have recomputed closeness centrality values for
each start-up in the open-deal list. Concretely, we extracted from CrunchBase.com a list of
101 companies that are labelled as venture capital firms see Table S5 for details.
Accordingly, in this experiment we create the WWS network but not include those nodes in the
network (and all the connections they bring with them). Closeness centrality is then evaluated
each month as described in the recommendation method. Results of overall success rate are
shown (green bars) in Fig.S15 while monthly success rates are compared in Fig.S17. The
success rate of the recommendation method based on this quantity is consistently similar to the
one found in the case where venture capital funds are not removed from the original network,
hence confirming that the topological presence of venture capital funds is not a confounding
factor.
S5.6 Possible confounding factor 2: number of employees
A second possible confounding factor or hidden predictor is the start-up size (e.g., number of
employees). To assess this possibility, we have conducted a number of experiments. Initially,
we explored start-up size (number of employees) instead of topological network centrality as
the informative predictor, and built a recommendation method based on that metric. Results are
shown in the left panel of Fig.S18, confirming that number of employees is not informative of
the start-up success likelihood.
Additionally, we have also checked the recommendation method (based on closeness centrality)
42
Figure S18: Accounting for start-up size. (Left panel) Monthly success rate of an hypothethi-
cal recommendation method based only on start-up size (number of employees), focusing in the
Top 20 start-ups in the open-deal list. Results wildly fluctuate above and below a random ex-
pectation model, and p-values safely conclude that the number of employees is not informative
of the start-up success likelihood. (Right panel) Monthly success rate of the recommendation
method based on closeness centrality, focusing in the Top 20 start-ups from a subset of the
open-deal list gathering only start-ups with a single employee. Results are qualitatively similar
to the ones obtained without conditioning for start-up size, and suggest that start-up size is not
a confounding factor.
when only the subset of open-deal start-ups with a fixed number of employees is considered.
Since the most frequent size is a start-up with a single employee, we extract the subset of all
start-ups with only one employee. Monthly success rates of the recommendation method are
shown in the right panel of Fig.S18. These results confirm that start-up size is not a counfound-
ing factor and that number of employees is indeed not an informative variable that determines
future success.
S5.7 Possible confounding factor 3: start-up geographical location
A third possible confounding factor is the geographical location of each of the start-ups. To
account for this, we have replicated our analysis (originally performed at a worldwide scale)
in five geographically separated regions, by dividing open-deal start-ups in five subsets: Cal-
43
ifornia, United Kingdom, New York, Texas and Israel. Results for the monthly success rate
of our recommendation method are plotted in Fig.S19. While results are more noisy than for
the worldwide setup, we can confirm that for every case the recommendation method based on
closeness centrality is above the random expectation.
S6 From recommendation to prediction of start-up success:
supervised learning approaches
The recommendation method proposed in the main text is based on the working hypothesis that
start-ups with higher closeness centrality rankings are more likely to experience a economic
successful outcome in the future. We have provided theoretical foundation to our research hy-
pothesis at the microscopic level, and then heuristically validated our recommendation lists on
a monthly basis, obtaining results that are significantly better than those obtained by a random
expectation model.
However, strictly speaking, a recommendation method is not a true prediction method, as we
are not predicting the outcome of each and every start-up in the open-deal list (either to the
successful or to the non-successful category). To bridge this gap, in this section we consider
different types of prediction models which can indeed truly “predict” the positive outcome of a
start-up, i.e. they can classify whether a given start-up will have a positive outcome or not.
All models are initially based on a sample including 5,305 firms. These are the firms that have
been in the open-deal list for at least one month, and can therefore be suggested as potential
investment opportunities. Each firm is then observed over a period of 24 months, or until when
it has experienced a “successful” event (positive economic outcome) if this event occurs before
the end of the 24 months period. Notice however that in the greatest majority of cases firms were
observed for 24 months. For this experiment note also that we are aggregating all the firms in
open-deal list in our database: not all of them are observed in the same time, e.g. one firm can
44
Figure S19: Accounting for spatial location. Monthly success rate of recommendation method
on five geographically separated regions.: California, United Kingdom, New York (US), Texas
(US) and Israel. For the California ecosystem we considered the Top100 ranking whereas for
the other four (smaller) ecosystems we only considered the Top 10. Results are more noisy
by qualitatively similar to the ones obtained in the original case, hence confirming that spatial
location is not a confounding factor.
45
be observed for the 24 months starting in January 2000, another firm can be observed for the
24 months starting in June 2004, etc. In other words, month t= 1 for a given firm does not
necessarily matches the actual date of month t= 1 for another firm, we are simply recording
the temporal evolution of different start-ups which appear in open-deal lists at different times in
the period ranging from 1990 to 2008.
Then, for each of the 5,305 firms, we conclude that a firm has experienced a “successful” event
(a positive economic outcome) at month tif, within a time window of t= 6,7or 8years
since month t, one of the following events takes place: (i) the firm makes an acquisition; (ii) the
firm is acquired; or (iii) the firm undergoes an IPO. Accordingly, each firm receives a unique
class label (either successful with class label ‘1’, if at any time t+ ∆tthe start-up experiences
a successful event, or not-successful with class label ’0’ otherwise).
Overall, this data set enables supervised learning (classification), as it consists of a large number
of samples (the firms in the open-deal list), each of them described by a set of features (a vector
of centrality measures over the whole observation window), and each of them being labelled by
a class label.
We will use logistic regression as our supervised learning model. A logistic regression model
links the probability of success of a start-up to a linear combination of predictors. More pre-
cisely, a logistic regression model is traditionally given by:
log pi
1pi=βTXi+εi(S4)
where piis the probability of success of the i-th start-up, Xiis the vector of predictors, βTis
the (transposed) vector of parameters, which are estimated when the logistic regression model
is fitted, and εiare the errors, which are assumed to be independent, identically-distributed
46
Normal random variables. Rearranging terms, we have
pi=σ(βTXi+εi),
where βTXi+εiis a linear combination of predictors with additive noise term and σ(x) =
1/[1 + exp(x)] is the so-called logistic function. In essence, the term βTXi+εiis akin to a
linear regression on the predictors, and the logistic function is used to force the outcome to be
equal to 0 or 1: if pi< c, the class 0is assigned, and for pi> c the class 1is assigned, where
the threshold cis indeed another parameter that can be trained by the algorithm. Once the pa-
rameters are estimated, logistic regression can be used to predict the probability of success of
new start-ups.
In what follows we consider two scenarios. In the first case, we define prediction models that do
not consider the time evolution of centrality measures for each firm and only use instantaneous
values of the firm’s closeness centrality: these models will be closer in spirit to the recommen-
dation method. In a second case, we enrich the predictor set by adding predictors summarising
the time evolution of the firm’s centrality over the observation period (to assess whether this
factor is informative) as well as similar quantities extracted from different centrality measures.
S6.1 Logistic regression: the unbalanced case.
Here we use the ROC (receiver operating characteristic) curve to assess the efficacy of this
binary classification algorithm to choose the optimal threshold based on our tolerance for false
negatives and desire for true positives. We initially have used only the last value of the (rescaled)
closeness centrality of a start-up over the observed period as the single predictor, in order to try
to match the conditions of our recommendation method where only instantaneous information
is used. The estimation and prediction steps above have been repeated 1,000 times, leaving out
10% of the data set (Monte Carlo cross-validation). Averaging over the prediction results, we
47
obtain the confusion matrix reported in Table S2 (left panel), together with the confusion matrix
expected for a random classifier operating on the same data set (right panel).
ACTUAL predicted
failure success
true failure 0.43 0.34
success 0.11 0.13
RANDOM predicted
failure success
true failure 0.593 0.177
success 0.177 0.053
Table S2: (Left) Confusion matrix for a logistic regression based on the last value of close-
ness and on the mean closeness over the entire period in the unbalanced case. Averages over
1,000 repetitions of the Monte Carlo cross-validation leaving out 10% of the data. (Right) Cor-
responding confusion matrix expected for a random classifier in the same unbalanced case.
Classical ways to assess the prediction performance include the evaluation of accuracy, de-
fined as the total percentage of correctly identified samples, sensitivity, defined as the percentage
of successful start-ups correctly predicted by the classifier over the percentage of true success-
ful start-ups, and precision, defined as the percentage of successful start-ups correctly predicted
by the classifier over the total percentage of start-ups which are predicted as successful by the
classifier. The F1 score is the harmonic average of precision and sensitivity. Depending on the
context, it might be desirable for a classifier to have high sensitivity or precision, and when both
quantities are relevant then the F1 score is typically used to assess model selection. In our case
the sensitivity is the relevant quantity to look at if we want to maximise the detection of success-
ful start-ups, whereas the precision is important if we want to make sure that all the start-ups
classified as successful will be successful. In other words, the first performance indicator can
be the one of relevance for an investment company with unlimited budget, while the precision
can be of interest to an investment company with limited budget.
The values obtained for the different indicators are reported in Table S3. The F1 score
–which trades off sensitivity and precision– shows that the predictions on whether any start-
up in the open-deal list will have a positive outcome are systematically better than those of a
benchmark given by a random classifier. Note that the problems with the accuracy are due to
48
the fact that our two classes are unbalanced, and this can affect the usefulness of this indicator.
We will come back to this point in the next subsection.
We have also experimented by including additional features of the evolution over time of the
closeness centrality as predictors in the logistic regression model. Interestingly, our results
did not improve significantly, suggesting that it is not necessary to use temporal evolution of
centrality measures, and thus confirming the validity of the recommendation method. This
observation will be further explored in the next subsection.
Accuracy Sensitivity Precision F1 score
Unbalanced 0.56 0.54 0.28 0.37
Unbalanced (random classifier) 0.65 0.31 0.31 0.31
Balanced (single predictor) 0.58 0.61 0.57 0.59
Balanced (with temporal information) 0.59 0.62 0.58 0.60
Balanced (random classifier) 0.5 0.5 0.5 0.5
Table S3: Summary of the performance indicators obtained for a logistic regression model to
predict the success of start-ups in the open-deal list based on the last and on the mean value of
closeness over time. Both unbalanced and balanced cases are considered.
S6.2 Logistic regression: the balanced case
It is well known that many binary classification algorithms suffer if the two classes are un-
balanced, i.e. if the number of samples in each class is not similar. A classifier would then
systematically try to fit the over-represented class and, as an outcome, the classification would
be biased. Consider, e.g., the extreme case where the classifier assigns each sample to the over-
represented class. In this extreme situation, the classifier would not be predicting anything, but
the classification accuracy would still be very high due to class unbalance. For such a reason
most classifiers do not perform well for unbalanced classes, and in unbalanced classification,
accuracy can be a misleading metric. This is indeed our case, as in our data set the majority
of start-ups do not end up being successful. Here, we show that, when we correct for class un-
balancing, then the prediction performance substantially improves. In order to solve the issue
49
of unbalanced classes, we downsample the over-represented class, so that the successful/non-
succesful classification problem has now perfectly balanced (50% 50%) classes.
All over this section we use 5-fold crossvalidation. First we have considered that case where
we only use the value of the closeness centrality of each start-up in the last month of our ob-
servation window, this being closer in spirit to the analysis performed in the main part of the
manuscript. Again, the descriptor used is the closeness centrality rescaled ranking. The perfor-
mance indicators of this logistic regression model are reported in Table S3, while the confusion
matrix is shown in Table S4. Results confirm that prediction is indeed possible, and performance
indicators are safely superior to random benchmarks.
ACTUAL predicted
failure success
true failure 0.275 0.227
success 0.193 0.305
RANDOM predicted
failure success
true failure 0.25 0.25
success 0.25 0.25
Table S4: (Left) Confusion matrix for a logistic regression with a single predictor in the bal-
anced case , using 5-fold cross-validation. (Right) Equivalent confusion matrix expected for a
random classifier in the same balanced case.
We have also considered a second logistic regression model with predictors including various
statistics of the temporal sequence of closeness centralities in the observation window. We have
used the following 9 predictors based on closeness centrality, namely: maximum value, mini-
mum value, slope of a linear interpolation and last value of both the ranking and the rescaled
ranking, and number of months in the observation window). The model provides an accuracy
of 0.59, sensitivity 0.62 and precision 0.58, indicating that temporal information leads to only a
marginal improvement over the previous case.
Finally, we have investigated other logistic regression models by further adding predictors re-
lated to other centrality measures. We find that the performance is not boosted, in agreement
with the fact that in our case most of the other centrality measures tend to be correlated to the
closeness, according to Fig.S11.
50
3i group advanced technology ventures accel partners
andreessen horowitz atlas venture atomico
august capital austin ventures avalon ventures
azure capital partners bain capital ventures balderton capital
battery ventures benchmark bessemer venture partners
binary venture partners canvas venture fund carmel ventures
charles river ventures clearstone venture partners columbus nova
costanoa venture capital crosslink capital crunchfund
data collective digital sky technologies fo draper fisher jurvetson
elevate ventures ff venture capital fidelity ventures
firstmark capital first round capital flybridge capital
foundation capital founders fund general catalyst partners
genesis partners golden gate capital ggv capital
google ventures granite ventures greylock partners israel
harris harris group highland capital partners idg ventures europe
idg ventures india idg ventures vietnam initial capital 2
in q tel index ventures innovacom
insight venture partners intel capital intellectual ventures
institutional venture partners inventus capital partners jerusalem venture partners
jmi equity kapor capital kleiner perkins caufield byers
khosla ventures lightspeed venture partners lux capital
matrix partners maveron mayfield fund
menlo ventures meritech capital partners merus capital
morgenthaler ventures new enterprise associates norwest venture partners
oak investment partners oregon angel fund openview venture partners
polaris partners radius ventures redpoint ventures
revolution capital partners rho ventures finisterre capital
rre ventures rothenberg ventures sante ventures
scale venture partners scottish investment bank scottish equity partners
sequoia capital seventure partners sevin rosen funds
the social capital partnership sofinnova partners spark capital
tenaya capital third rock ventures tribeca global investments
union square ventures us venture partners vantagepoint capital partners
venrock wellington partners
Table S5: List of 101 venture capital funds extracted from crunchbase.com. Also available
at https://en.wikipedia.org/wiki/List_of_venture_capital_firms.
51
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os, A. R´
enyi, On random graphs I. Publicationes Mathematicae,6, 290-297 (1959).
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31. S. B. Seidman, Network structure and minimum degree. Social Networks,5(3), 269-287
(1983).
32. S. Wasserman, K. Faust, Social Network Analysis: Methods and Applications (Cambridge
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