Conceived and designed the experiments: XFL XKX MS CKT. Performed the experiments: XFL. Analyzed the data: XFL XKX MS CKT. Contributed reagents/materials/analysis tools: XFL. Wrote the paper: XFL XKX MS.
The authors have declared that no competing interests exist.
Stationary complex networks have been extensively studied in the last ten years. However, many natural systems are known to be continuously evolving at the local (“microscopic”) level. Understanding the response to targeted attacks of an evolving network may shed light on both how to design robust systems and finding effective attack strategies. In this paper we study empirically the response to targeted attacks of the scientific collaboration networks. First we show that scientific collaboration network is a complex system which evolves intensively at the local level – fewer than 20% of scientific collaborations last more than one year. Then, we investigate the impact of the sudden death of eminent scientists on the evolution of the collaboration networks of their former collaborators. We observe in particular that the sudden death, which is equivalent to the removal of the center of the egocentric network of the eminent scientist, does not affect the topological evolution of the residual network. Nonetheless, removal of the eminent hub node is exactly the strategy one would adopt for an effective targeted attack on a stationary network. Hence, we use this evolving collaboration network as an experimental model for attack on an evolving complex network. We find that such attacks are ineffectual, and infer that the scientific collaboration network is the trace of knowledge propagation on a larger underlying social network. The redundancy of the underlying structure in fact acts as a protection mechanism against such network attacks.
Many natural and man-made complex systems such as biological networks, the WWW, airport network and stock markets network, evolve intensively at the local level
On the other hand, it has been widely observed that many stationary networks are robust to random failure but vulnerable to targeted attacks
In this paper we analyze the collaboration network of US-based life scientists to address two main topics. First, we examine the topological evolution of the network and show that the scientific collaboration network is intensively evolving. When compared to recently proposed theoretical models of such networks
Collaborations between scientists do not last forever. In the scientific collaboration network – where nodes are scientists and links are collaborations – the network can therefore have drastically different constitution when sampled in different time intervals. In this section we study the topological evolution on the collaboration network first by examining the life span of scientific collaborations. Five thousand scientists are sampled from the AAMC Faculty Roster according to the criteria that their academic life spans are longer than 10 years and each of them has more than 10 collaborators. By using this criterion, we actually assure that the life span of collaboration will not be restricted by the observation period. Then by retrieving their publications from PubMed, the life span and productivity (in term of numbers of journal articles published) of each pair of collaboration can be studied.
(A) The probability distribution
(A) The probability distribution
To fully characterize the dynamics of the topological network evolution, egocentric scientific collaboration networks are constructed based on a sliding window. The egocentric network of a scientist contains the scientist and his/her first tier collaborators, i.e. the scientists co-authored papers with him/her, and/or the second tier collaborators, i.e. the co-authors of the first tier collaborators excluding the center scientist him/her-self, within a certain period of time. Here we consider the egocentric networks in two different scales:
T-1 network: (i) the center node (the scientist) and (ii) its first tier neighbors;
T-2 network: (i) the center node (the scientist), (ii) its first tier neighbors and (iii) second tier neighbors.
Then we define the
(A) and (B) are the T-2 egocentric scientific collaboration networks of the same eminent scientist in two consecutive non-overlapping time windows (window size = 5 years). The red node is the center of the network, i.e. the superstar. The blue and gray nodes are the first and second tier neighbors of the superstar in that particular time window. The sizes of the nodes and thickness of the edges in the figure are proportional to the numbers of journal articles published by the scientists and the numbers of journal articles co-authored by the pairs of collaborations. (C) is the T'-2 network after the superstar's death. The blue nodes are the dead superstar's first tier neighbors in the last window before his death (the former collaborators). The gray nodes are the neighbors of the former collaborators in the first window after the superstar's death.
Once the egocentric networks of all windows are formed, we measure the scale and connectivity of the networks with four parameters: numbers of nodes
The clustering coefficient measures the conditional probability that two scientists may collaborate if they both collaborate with same (third-party) scientist. The network efficiency
Figures labeled A–B and C–D represent two scientists respectively. A and C: Numbers of nodes
Previous research of the US airport network
Recent studies have shown that, following the death of an eminent life scientist (“superstar”), collaborators experience a 5% to 8% decline in their publication rates
Twenty one superstars who died unexpectedly are selected as the subject of our study. We define the “former collaborators” of a dead superstar as the superstar's direct collaborators in five years preceding death. To study the impact of the superstars' sudden death, we compare the collaboration networks of the former collaborators in the last 5 years before the superstar's death and in the first 5 years afterwards. The T-1 and T-2 egocentric networks of the dead superstars in the last window characterize, respectively, the collaboration among the former collaborators and their collaboration networks right before the death of the superstar. Then, in the first 5-year window after the superstar's death, two new networks T′-1 and T′-2 are constructed analogously to T-1 and T-2 networks, as shown in
Having constructed the former collaborators' collaboration networks in two consecutive windows, we measure the changes (Δ
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|
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T-1 (before death) | 12.57 | 28.24 | 0.48 | 0.75 |
T'-1 (after death) | 10.33 | 4.57 | 0.08 | 0.11 |
Change in % | −18% | −84% | −83% | −86% |
T-2 (before death) | 81.57 | 203.90 | 0.48 | 0.43 |
T'-2 (after death) | 105.29 | 306.81 | 0.51 | 0.21 |
Change in % | +29% | +50% | +7% | −50% |
Average values of network parameters (i.e. number of nodes
This result suggests that the sudden deaths of the superstars have stimulated their former collaborators to rearrange their networks in an efficient manner. To determine whether the impact of sudden death is significantly different from the natural network evolution (i.e. without the sudden death of the superstar), two non-parametric statistical tests are conducted.
The results of the measured parameters are summarized in
Change between | Δ |
Δ |
Δ |
Δ |
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Test 1 ( |
T'-1 and T-1 | 21/21 | 20/21 | 21/21 | 21/21 |
T'-2 and T-2 | 21/21 | 20/21 | 20/21 | 21/21 | |
Test 2 ( |
T'-1 and T-1 | 0.52 | 0.45 | 0.68 | 0.36 |
T'-2 and T-2 | 0.27 | 0.24 | 0.22 | 0.53 |
The test results of Test 1 (
In
Our statistical tests show that there is no evidence that the sudden death of a superstar may have a significant impact on the evolution of its collaborators' scientific collaboration networks. Previous research shows that improving the robustness of diverse networks often involves increasing the redundancy of the network at critical positions
Of course, the premature deaths of eminent scientists may be considered a great loss to their particular discipline. Nonetheless, it is known that after the (unanticipated) deaths of some eminent scientists, the scientific productivity of collaborators suffer from a 5% – 8% drop. In this paper we have examined, from another aspect, the impact of the sudden deaths of these superstars to the structure evolution of their former collaborators' collaboration networks. We have firstly shown that the scientific collaboration network is a complex system which intensively evolves at the local level. Most collaborations among scientists have short life spans and the relative incidence of long term collaboration is very low. We have compared the behavior of network evolution between collaborators of suddenly deceased eminent scientists and active ones. Surprisingly, statistics show that the evolution of collaborators' networks are not affected by the sudden deaths of the superstars.
In particular, we have observed that the egocentric scientific collaboration networks evolve in such a manner that: direct collaborators of a superstar in one period of time tends not to collaborate with each other in the next, whereas the collaborators' own egocentric networks grow bigger. This evolution pattern is actually an analogy to the diffusion process on an arbitrary form of network, where nodes can generate a stimulus and spread it out to their first then second tier neighbors and so on. Hence we conjecture that, rather than mapping the social networks of scientists, the scientific collaboration network is actually the “trace” of information propagation on a larger and denser invisible social network than the trace itself.
Actually the trace of information propagating and disease spreading in human society share the same evolution mechanism with scientific collaboration network and that the redundancy of the underlying social structure in fact acts as a protection mechanism when these networks are under attack. From this perspective, future study of effective network attacks (such as immunization strategies) should consider the underlying rapid evolving social structure. Moreover, the designing of robust information transmission systems could also gain from the robust system formed by human social and collaborative endeavors. For example in the Internet, routing strategies with constantly changing paths between nodes might give extra robustness to the system even under targeted attacks.
In this paper the collaborations of three groups of US based life scientists are studied. The first group are the scientists listed in the Faculty Roster of the Association of American Medical Colleges until the end of 2010. The second group contains 77 eminent life scientists (“superstars”), including (i) current members of National Academy of Sciences major in life science; (ii) emeritus members of National Academy of Sciences major in life science; (iii) top 500 highly cited life scientists retrieved from ISI Web of Knowledge until the end of 2010. Moreover all of the 77 scientists had been active in their academic life for not less than 10 years and had collaborated with not less than 20 other scientists in the Faculty Roster. The third group of scientists are 21 life scientists who died unexpectedly and prematurely in the early stage of their scientific career and had comparable academic achievements with the previous group of superstars at the time of their death
Scientists are connected only when they co-author a journal article. The publication information are retrieved from online database PubMED, which is provided by the National Library of Medicine and stores intact biomedical research literature. The authors' names in PubMED are stored in the form of name identifier which takes the initials of the first names and the whole last name, i.e. Xiao Fan Liu is stored as XF Liu. However in the Faculty Roster which stores the full names of all the faculties, some of the names may have the same identifiers. For example the identifiers of John Doe and Jane Doe are all J Doe. Hence from the information provided by PubMED we cannot determine whether a paper published by J Doe is actually written by John Doe or Jane Doe. In our work, different names with the same identifiers are eliminated from the Faculty Roster, thereby reducing the size of the Faculty Roster to 112,753.
The superstars are not only excellent in their academic achievements but also important in terms of network measure in the network of scientists. Constructing a scientific collaboration network covering all the publications the scientists have in their life time,
The degree distributions of 7555 samples from the Faculty Roster, 77 eminent life scientists and 21 suddenly died eminent life scientists are shown in the figure. The average degree of the three groups are 31.83, 56.56 and 35.29.