Zhao et al. EPJ Data Science(2020) 9:7
https://doi.org/10.1140/epjds/s13688-020-00224-z

REGULAR ARTICLE

Open Access

Fake news propagates differently from realnews even at early stages of spreading
Zilong Zhao1,2† , Jichang Zhao3† , Yukie Sano4† , Orr Levy5† , Hideki Takayasu6,7 , Misako Takayasu7 ,Daqing Li1,2* , Junjie Wu3,8* and Shlomo Havlin5,7*

Correspondence:
daqingl@buaa.edu.cn;
wujj@buaa.edu.cn
1School of Reliability and Systems
Engineering, Beihang University,
Beijing, China
3
School of Economics andManagement, Beihang University,
Beijing, China
Full list of author information isavailable at the end of the article†
Equal contributors

Abstract
Social media can be a double-edged sword for society, either as a convenientchannel exchanging ideas or as an unexpected conduit circulating fake news througha large population. While existing studies of fake news focus on theoretical modelingof propagation or identiﬁcation methods based on machine learning, it is importantto understand the realistic propagation mechanisms between theoretical models andblack-box methods. Here we track large databases of fake news and real news in
both, Weibo in China and Twitter in Japan from diﬀerent cultures, which include theirtraces of re-postings. We ﬁnd in both online social networks that fake news spreads
distinctively from real news even at early stages of propagation, e.g. ﬁve hours after
the ﬁrst re-postings. Our ﬁnding demonstrates collective structural signals that help
to understand the diﬀerent propagation evolution of fake news and real news.
Diﬀerent from earlier studies, identifying the topological properties of the information
propagation at early stages may oﬀer novel features for early detection of fake news
in social media.
Keywords: Fake news; Social network; Early detection

1 Maintext
Social networks such as Twitter or Weibo, involving billions of users around the world,
have tremendously accelerated the exchange of information and thereafter have led to
fast polarization of public opinion [1]. For example, there is a large amount of fake news
about the 3.11 earthquake in Japan, where about 80 thousand people have been involvedin both diﬀusion and correction [2]. These fake news, which can be fabricated stories
or statements yet without conﬁrmation, circulate online pervasively through the conduitoﬀered by on-line social networks. Without proper debunking and veriﬁcation, the fastcirculation of fake news can largely reshape public opinion and undermine modern society[3]. Even worse, fake news can be intentionally fabricated, leading to diverse threats tomodern society including turmoil or riot. The later fake news is identiﬁed and corrected
the greater the damage it can make, due to its fast propagation. Thus, detecting fake news
at their early stages, in order to eﬀectively avoid further risks and damages, is crucial.
Diﬀerent from the age of word of mouth, identiﬁcation of fake news in the online social network by experts is generally labor-intensive with low eﬃciency [4], which has at© The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use,sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original
author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or otherthird party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted bystatutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view acopy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Zhao et al. EPJ Data Science(2020) 9:7

tracted much research attention to provide alternative solutions. One intuitive idea forunderstanding fake news spreading is inspired by epidemic models. In the 1960s, Daleyand Kendall proposed the so-called DK model [5] in which agents are divided into ignorant, spreader and stiﬂe. Its later extensions are based on the known epidemic spreading
models such as SIS model [6, 7], SIR model [8, 9], SI model [10, 11] and SIRS model [12].
While these studies focus on theoretical modeling of fake news propagation, the availability of real data in online social platforms, as we show here, can provide an opportunity
to deepen our understanding of the realistic information cascades. Diﬀerent kinds of observations have been made in empirical studies of fake news, including linguistic features[13], temporal features of re-postings [14–16] and user proﬁles [17–19]. Actually, information cascades in online social networks are collective propagation networks of which
critical topological features remain yet unknown. This motivates our present study to analyze and compare empirically the propagation networks between fake and real news, especially in their early stage, so as to identify the propagation diﬀerences and mechanisms
behind. These topological features could help to design machine learning approaches toessentially boost the accuracy of fake news targeting [20–22].
Very recently, based on empirical datasets, it has been found that the propagation network of fake news is diﬀerent from that of real news [23]. They have found that falsehood
propagates signiﬁcantly farther, faster, deeper, and broader than truth news in many categories of information. While this study provides the possibility to diﬀerentiate fake news
from real news based on the propagation network, it remains unclear how this diﬀerence
between fake news and real news emerges and how soon one can separate these two types.
Thus, a systematic study for the dynamic evolution of propagation topology is still missing. This motivated us to explore deeper in this direction of how the propagation evolves
topologically in diﬀerent scenarios. With collected real data, we identiﬁed early signals for
identifying fake news, at ﬁve hours from the ﬁrst re-posting, without other information oncontents or users. Note that diﬀerent from considering all the cascade components [23],our ﬁnding is valid for even only following the largest cascade component.
Based on realistic traces of real and fake news propagation in both Weibo (from China)
and Twitter (from Japan), we use the re-posting relationships between diﬀerent users toestablish propagation networks (see Methods for details). Given similar popularity scales,
we ﬁnd that fake news shows signiﬁcant diﬀerent topological features from real news.
These novel topological features will enable us to design an eﬃcient algorithm to distinguish between fake news and real news even shortly after their birth.

2 Results
To construct the propagation network of fake and real news, we utilize the re-posting relation between diﬀerent users participating in circulating the same message (see Methods
and Table 1). A schematic description of such propagation networks is shown in Fig. 1A.
Typical propagation networks of fake news and real news in Weibo and Twitter are demonstrated in Fig. 1B–E. The topology of the propagation network of fake news and real news
can be seen to be diﬀerent. For example, the number of layers in fake news (Fig. 1B and 1D)
is typically larger than that of real news (Fig. 1C and 1E). Additionally, from looking at various examples of fake news propagation networks, it is somewhat surprising that for widelydistributed fake news, the creator does not usually have the largest degree in the propagation network (Figs. S1 and S2). In the following, our analysis considers also real news

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Table 1 Number of users and networks for diﬀerent propagation networks

Weibo users in the whole dataset
Twitter users in the whole dataset
Number of Weibo propagation networks (larger than 200 re-postings)
Number of Weibo propagation networks which can be studied at ﬁvehours (larger than 200 re-postings)
Number of Twitter propagation networks (larger than 200 re-postings)

Fake news

Real news

973,391
105,335
1701
1578

347,401
133,109
492
448

27

28

The Weibo networks are from the ﬁrst Weibo datasets.

Figure 1 Typical examples of fake and real news networks. (A) Schematic diagram of the propagation of apost and its re-posting. The nodes represent the users and the edges are the re-postings. The directionality
determines which user is the re-poster among the two users: the origin is the former re-poster and the target
is the later re-poster. A layer consists of re-postings whose re-posters have the same distance from the creator.
We color the edges according to their layer from light to dark blue. (B) A real typical Weibo network of fakenews with 1123 nodes. The edge’s arrow stands for its direction. This fake news is about health problems due
to a milk tea shop. (C) A typical Weibo real news network with 215 nodes. This is about a tip of preventing
sunstroke. (D) A typical Twitter fake news network with 199 nodes. This tweet is about an electric store thatraised the price of a battery unreasonably. (E) A typical real news network on Twitter with 578 nodes. This
tweet is a correction tweet against fake news about Cosmo oil by the Asahi newspaper. We applied the
Fruchterman–Reingold layout by using Pajek software here

Zhao et al. EPJ Data Science(2020) 9:7

Figure 2 Diﬀerent layer sizes as a function of time in typical networks. The y axis is the cumulative number of
re-postings at diﬀerent layers of typical networks in Weibo and Twitter. The x axis is the time (in hours) fromthe time of news creation and the diﬀerent colors stand for diﬀerent layers. Shown examples are (A) fake newsand (B) real news in Weibo, as well as (C) fake news and (D) real news on Twitter. These four typical networks
are the same networks shown in Fig. 1. In Fig. 2A, the fraction of nodes located in the ﬁrst layer is around 45%
of all the nodes at the end of propagation. However, in Fig. 2B, the total number of nodes in the ﬁrst layer
occupies about 78% of all the nodes at the end of propagation. If the total number of nodes does not changemuch after 20 hours, we ignore the re-posting after 20 hours in order to clearly see the layers in the ﬁgure. It isseen that the layer sizes of real news and fake news are signiﬁcantly diﬀerent in both Weibo and Twitter. Realnews networks tend to have a relatively larger ﬁrst layer, while fake news networks are relatively uniformly
distributed in diﬀerent layers

created by non-oﬃcial sources, to avoid the artiﬁcial diﬀerences due to diﬀerent types of
information creators (oﬃcial or non-oﬃcial accounts).
Layer ratio. The layer number is deﬁned as the number of hops from the creator to agiven node for a given propagation network. The cumulative numbers of nodes at diﬀerent
layers as a function of time for four typical networks of fake news (Fig. 2A for Weibo and
2C for Twitter) and real news (Fig. 2B for Weibo and 2D for Twitter) are demonstrated. The
fraction of re-postings in the ﬁrst layer of fake news network is found signiﬁcantly smaller
than that of real news, while the fraction in other layers for fake news is signiﬁcantly larger
than that of real news. Early adopters re-posting the message shortly after the creatorplay a dominant role in circulating real news comparatively. These diﬀerent roles lead to
distinctive landscapes of propagation networks.
The investigation of layer sizes in propagation networks demonstrated in Fig. 2, are systematically extended to all the available messages. As shown in Fig. 3A and 3B, fake news
networks tend to possess a relatively smaller ﬁrst layer, while other layers are larger comparatively. Therefore, we can deﬁne the ratio of layer size as the ratio between the size ofthe second and the ﬁrst layer. As shown in ratio distribution (Fig. 3C and 3D), the ratio in

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Figure 3 Ratio of layer sizes diﬀerentiates fake news from real news. The distribution of the ratio of layer sizes
and its development after a period of time can diﬀerentiate fake news from real news. These diﬀerences
appear already after a few hours. (A) The PDF of all re-postings in the ﬁrst ﬁve layers averaged over all of the
Weibo propagation networks. The p-value of Mann–Whitney is below 0.01. (B) The PDF of all re-postings in
the ﬁrst ﬁve layers in all networks of Twitter. The p-value of Mann–Whitney is below 0.01. (C) Distribution of
the ratio of layer sizes at ﬁve hours from the ﬁrst re-posting. The ratio of layer sizes is the size of the second
layer divided by the size of the ﬁrst layer. The p-value of Mann–Whitney between fake and real news is below
0.01. This ﬁgure considers all 1701 fake news, all 492 real news and 51 real news with non-oﬃcial creators at
ﬁve hours from the ﬁrst re-posting. (D) Distribution of the ratio of layer sizes of all re-postings for the wholelifespan. The p-value between fake and real news is below 0.01. Here we consider all available Weibo
propagation networks (all 1701 fake news, all 492 real news and 51 real news with non-oﬃcial creators)

fake news is signiﬁcantly larger than that of real news. The distribution for the ratio of layer
sizes separates fake and real news well with only a small overlapped area. Furthermore, it
is seen in Fig. 3C that this diﬀerence is already signiﬁcant only at ﬁve hours since the ﬁrst
re-posting. In Fig. 3D, it is seen that, for the whole lifespan, the separation of the fake andthe real is also signiﬁcant. In the circulation of fake news, the success of the propagation
depends highly on the branching process creating diﬀerent layers, which show diﬀerent
evolution paths between fake and real news. We further investigate the probability diﬀerence between fake and real news based on distributions of layer ratio from the time of ﬁrst
re-posting (Figs. S3 and S4). Note that the layer size distribution has a peak around layer
four on Twitter in Fig. 3B, probably due to secondary outbreaks.
It should be noted that real news is more likely to be created by oﬃcial accounts such as
government agencies or mass media agencies. In order to eliminate the possible eﬀects ofoﬃcial creators, we also investigate the distribution of the ratio of layer sizes in real news
from only non-oﬃcial creators. While oﬃcial news and non-oﬃcial news have diﬀerent
sample sizes here, we found they both have diﬀerent propagation patterns from fake news.
For example, in Fig. 3C and 3D, the non-oﬃcial real news and the fake news are found tohave diﬀerent distribution of layer size ratio. To verify our results, we also analyze data

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Figure 4 Characteristic distance diﬀerentiates fake news from real news. (A) The PDF of distances for three
typical examples of networks for both fake and real news in Weibo. (B) The PDF of distances for all real andfake news networks in Weibo. (C) The PDF of distances of all real and fake news networks in Twitter. (D) The
PDF of the characteristic distances (details in Methods) for fake news and real news. The p-value between fakeand real news is below 0.01

of 2000 more real news from non-oﬃcial accounts in a more recent dataset from 2016 to2018 shown in Figs. S5 and S6. The distributions of this real news dataset are also distinct
from that of fake news.
Characteristic distance. While the ratio of layer sizes can be regarded as a local featureof the network structure, we further inspect a global feature in terms of characteristic distance in a propagation network. As seen in Fig. 4A, distances between pairs of nodes infake news are longer than those of real news, implying that later adopters foster the penetration of fake news in social networks. In order to quantify this ﬁnding for all the networks, we propose a second measure called characteristic distance (a) shown in Fig. 4B(see Methods). Considering the distance of all the networks as in Fig. 4B, fake news possesses a signiﬁcantly longer characteristic distance (4.26) than that of real news (2.59).
Similar results can also be observed in Twitter propagations (Fig. 4C). The distributionsof characteristic distances for all networks are shown in Fig. 4D, where the two curves offake and real news are well separated. Diﬀerent from the results in [23], we show that thesize distributions of fake and real news are similar (Fig. S7). This suggests that with similarlevels of popularity, the characteristic distance is signiﬁcantly diﬀerent in fake news compared to real news. We also veriﬁed that the propagation size has less correlation with thecharacteristic distance (Fig. S8). To verify our results, we also analyze data of 2000 more
real news from another dataset shown in Fig. S5.
Structural heterogeneity. Network topology describes the geometry of connections, withmore information embedded than the scale statistics in [23]. Here we measure the Heterogeneity (see Methods) between propagation networks in fake and real news. The parameterh reﬂects the diﬀerence between a given propagation network and its counterpart of a star

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Figure 5 Heterogeneity measure for fake and real news in Weibo and Twitter. (A) The x axis is the size of the
propagation network, and the y axis is the heterogeneity measure of the networks. The black line is the valueof the star layout. The h is the diﬀerence of heterogeneity value between a real network and thecorresponding value of star layout. (B) The scatter plot like in (A) for Twitter. (C) Distribution of h at ﬁve hours
from the ﬁrst re-posting of the Weibo propagation networks. The p-value here is below 0.01. (D) Distributionof h of all re-postings in Weibo for the whole lifespan. The p-value is below 0.01

network with the same-size. Network with smaller h means similar to a star network. Although the out-degree distribution demonstrates only a minor diﬀerence between fakenews and real news (Fig. S9), it is interestingly found here that the topology heterogeneity
is signiﬁcantly distinguishable. Note that the relationship between heterogeneity and N
for star networks is power-law as seen in Fig. 5A. The h is the diﬀerence between the logarithm of a real network heterogeneity value Hr and the logarithm of heterogeneity valueof the same-size star network Hs . The parameter h of fake news is signiﬁcantly larger compared to that of real news. Consistent ﬁndings can also be observed on Twitter (Fig. 5B). In
order to quantify the heterogeneity systematically, two distributions of h considering different time intervals are calculated. In Fig. 5C, it shows a signiﬁcant diﬀerence at ﬁve hours
from the ﬁrst re-posting. For the whole propagation lifespan in Fig. 5D, h of fake news is
also signiﬁcantly larger than that of real news. Fake news networks have typically lower
heterogeneity (larger h) since their propagation involves few dominant broadcasters. On
the contrary, real news demonstrates higher heterogeneity (smaller h) and a more starlike layout. The ability to distinguish fake news from real ones is also valid for real news
posted by non-oﬃcial users (Fig. S10). This implies that the indicator based on structural
heterogeneity is independent of the creator type. Additionally, another measure named
the Herﬁndahl–Hirschman Index (HHI [24]) shows also a distinction between fake news
and real news (Fig. S11).
The distinction between fake and real news of the heterogeneity measure is the highest
among the above three indicators as seen in Fig. 6 and Table 2. For a given Weibo network,

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Figure 6 The heterogeneity measure shows a high diﬀerence between fake news and real news of Weibo in
its early stage of propagation. (A) Probability of being fake news at ﬁve hours. The three vertical lines divide
the ﬁgure into four parts with an equal number of networks. For example, the area on the left of the ﬁrst left
line has 25% of all the Weibo propagation networks. (B) Probability of being fake news for the whole lifespan.
(C) The diﬀerence signiﬁcance between fake news and real news

Table 2 Comparison between three methods
MeasureRatio of layer sizes
Characteristic distance
Heterogeneity (h)Diﬀerence signiﬁcance of Weibo
Whole lifespanFive hours

Non-oﬃcial creator

75.0%
74.6%
78.2%

74.4%
73.0%
74.1%

74.0%
70.1%
71.3%

The Weibo networks are from the ﬁrst Weibo datasets.

measuring its h provides a clear diﬀerence between fake news and real news, even only
considering re-postings at ﬁve hours from the ﬁrst re-posting (Fig. 6A). This identiﬁcation
becomes even sharper in Fig. 6B, when we consider all re-postings. We show in Fig. 6C thediﬀerence signiﬁcance (see Methods) between fake news and real news for diﬀerent h. The
diﬀerences are about 76% and 79% respectively for re-postings at a relatively short time
(ﬁve hours) and all re-postings. Note that the probability of being fake news at ﬁve hours
is already very similar to that for the whole propagation lifespan. The veriﬁcation analysis(shown in Figs. S5 and S6) also demonstrates the diﬀerence signiﬁcance between fake news
and real news from another dataset, which is fully published by non-oﬃcial accounts. Our
results suggest that even without sophisticated features like texts or user proﬁles, direct
and understandable topological features can oﬀer high signiﬁcance for developing early
detections.
Classiﬁer. The three features mentioned above, namely the ratio of layer sizes, the characteristic distance, and the heterogeneity parameter could be used to create a Support
Vector Machine (SVM) classiﬁer. Here we divide the dataset into training set (60%) andtest set (40%) ten times randomly. We ﬁnd that the average accuracy of this classiﬁer is
79.5% when applying the RBF kernel.

3 Discussion
Being the most vital and popular form of new media, online social networks, fundamentally enhance the creation and dissemination of fake news [25, 26]. Though existing solutions, especially the inspired machine learning approaches, perform impressively ontargeting fake news, their black-box style essentially prevents a solid understanding andcorresponding method development of debunking or blocking false information. On theZhao et al. EPJ Data Science(2020) 9:7

other way, the human-intensive labor approach is time-consuming and expensive. For example, it usually takes at least three days [4] for veriﬁcation and therefore misses the optimal prevention window before massive spreading. In this sense, novel approaches that
could help to identify fake news at early stages are urgently needed in preventing the negative impact of false information propagation on modern society.
We show here that fake news spread with very diﬀerent network topology, even at earlystages, from authentic messages. We focus, in this manuscript on the evolution diﬀerences between the propagation topology of two types of information at early stages rather
than providing a comprehensive prediction approach [22]. Even taking only one feature,
the diﬀerence between fake news and real news is signiﬁcant. The propagation mechanism, which essentially couples information dynamics and collective cognition in social
networks, results in a distinctive landscape of circulations between fake and real news. In
this way, several early signals can be derived, including the layer-ratio, the characteristic
distance and the heterogeneity. Varol et al. study early detection of promoted campaigns byusing supervised machine learning, which contains features about diﬀusion patterns, content information, sentiment information, temporary signals, and user data [27]. Moreover,
Vicario et al. study fake news by identifying polarizing content, which contains structuralfeatures, semantic features, user-based features and sentiment-based features [28]. In contrast, our suggested measures focus on structural features which are simple, without text
analysis, and time eﬃcient. For example, the weak heterogeneity of fake news might be
the result of opinion competition from weak ties between social communities. As statedthat “bad” is usually more inﬂuential than “good” [29], the unconsciousness of “negativebias” might result in a late burst of fake news, which essentially diﬀers from the spread ofreal ones. Disclosing intelligence factors that generate the speciﬁc topological features wefound here can be a promising research direction in the future. Moreover, once we identify fake news, it is possible to study the nodes that participated in many networks. These
nodes are much more active in the permeation of fake news, and as a result, they are more
likely to be bots. The study of these vital nodes in the fake news propagation will play animportant role in identifying and analyzing bots.
Note that our study has several major diﬀerences from Vosoughi et al. [23]. We focus
more on the topological features (shape of a network), rather than on scale measures of
propagation networks (depth or width). Furthermore, we focus on the largest cascade
component of the propagation network, while all the cascade components are consideredin [23]. As both manuscripts conﬁrm the diﬀerence between fake news and real news in
diﬀerent aspects, we ﬁnd surprisingly that this diﬀerence can be very signiﬁcant even at
the early stages of propagation.

4 Methods
Weibo data preprocessing. We analyze 1701 fake news of Weibo propagation networks(with 973,391 users) and 492 real news of Weibo propagation networks (with 347,401
users) that spread on Weibo from 2011 to 2016. We choose here large networks with morethan 200 tweets. More details are given in Table 1. The topics of these Weibo propagation
networks include political fake news, economic fake news, fraudulent fake news, tidbit
fake news and pseudoscience fake news (Fig. S12).
Fake news is oﬃcially investigated and conﬁrmed by the platform of Weibo [30]. Regarding real news, we collect them directly from reliable Weibo accounts. Creators of the

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real news can be oﬃcial accounts, for example, government accounts and on-line newspaper accounts. All these real news accounts have been oﬃcially veriﬁed by the platformof Weibo. On the other hand, we also select manually 51 out of 492 real news networks
whose creators are not oﬃcial accounts. To verify our results, we also analyze anotherdataset (2000 more recent real news) from Weibo in Figs. S5 and S6. These 2000 real news
networks are from more recent records that has been collected in the same way as above,and from non-oﬃcial accounts.
In order to create the network, in which nodes are users of Weibo and links are repostings, we ﬁrst mine the following data both for fake and real news:(a) Users: the unique serial number of users who participate in the same network. We
also mark the node of the network creator.
(b) Re-postings: the unique serial number of directed re-posting activities, and theserial number of source users and reposted users of this re-posting.
Twitter data preprocessing. Twitter data was collected from Japanese tweets posted during the period between March 11th and March 17th in 2011, which is the Great East Japan
earthquake period. During this period, a lot of fake news propagated on Japanese Twitter.
After gathering fake and real news tweets on a keyword basis, we focused on those withmore than 200 tweets to create a retweet network. Here we deﬁne screen names as nodes,
which appeared in the tweet context, and links are mention signs “@” between the authorof the tweet and screen names after the sign. This is because many fake retweet users havealready deleted their tweet or account itself, and do not appear in the database. Deletingthe tweet or account makes the network more segregated and more challenging to capture the real structure of the networks. To avoid network segregation, we use the abovementioned context-based method to create retweet networks. Furthermore, as of Marchin 2011, many Japanese Twitter users did not clearly distinguish between mention symbol“@” and clear retweet symbol “RT @”. Note that if there are multiple “@” in one tweet, according to the above rules, we extracted multiple screen names as nodes and linked themin order from the beginning of the sentence to create the networks. We compared two
types of networks deﬁned by mention symbol and retweet symbol in Fig. S13, and found
our major results still hold.
After creating networks, we extract the largest connected component (LCC) without
consideration of link directions and analyze only those with LCC size above roughly 200
nodes. A node with the oldest tweet time in LCC was treated as creators. All the fake andreal news that we determined are shown in Additional ﬁle 1.
Our method of creating a retweet network is diﬀerent from the way of previous literature [20, 23] that used follower graphs and tweet data simultaneously to create a retweet
network. In case that we do not have a follower graph as of 2011, we applied this approximate method of extracting as much information as possible from the tweet context. In
principle, because retweet information remains in the tweet context, the topology of the
network should be equivalent to the previous literature, but the time information in resolution of seconds is not accurate in our case. Therefore, we only use time information inhours in the Twitter analysis.
Deﬁnition of fake news and real news. In a recent paper by Lazer et al. [31], “fake news”
is deﬁned as fabricated information that mimics news media content in the form, without
news media’s editorial norms and processes for ensuring the accuracy and credibility of
the information. In our manuscript with Weibo data, the fake news is false information

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fact-checked by the platform and veriﬁed as having been fabricated. Regarding real news,
we collect them directly from reliable Weibo accounts. And all these real news accounts
have been oﬃcially veriﬁed by the platform of Weibo.
For Twitter data, the fake news is also false information which is fact-checked by reliable
evidences [32–34]. This is similar as the true/false news deﬁned in paper by Vosoughi etal. [23] that their rumor cascades are checked independently by six fact-checking organizations. However, since there were no oﬃcial anti-rumor website in Japan as of 2011, we
ﬁrst gathered 57 topics listed on websites [32, 33] and a book [34]. These contents include
tweets based on no evidence and malicious tweets, such as starvation of babies and elderly people, someone under the server rack needed help, and the Japan prime minister istaking luxury supper during the disaster. When collecting tweets, we combine a few keywords related to the contents of each fake news. These keywords were proper nouns, suchas place names and personal names. After that, we excluded correction tweets whose contents are against fake news including keywords such as “false” and “mistake”. Our typical
procedure to gather fake news tweets is explained in a previous work [2]. To validate thefake news tweets, three graduate students at the University of Tsukuba checked independently whether these topics are fake and the gathered tweets are properly classiﬁed into
fake news.
For real news in Twitter, we gathered 71 topics by combining keywords (proper nouns,
such as place names and personal names) as with the fake news. We collected most of
tweets originated from oﬃcial accounts with veriﬁed Twitter badges such as government agencies, major newspapers and famous people. The contents included tweets about
earthquake information, traﬃc information, donation information and so on. In addition,
we also collected ﬁve topics originated from civilians without badges, which were widely
retweeted. These tweet contents were related to small correct tips during the disaster.
Establishing a network model. Based on the information we analyze above, we establish
a directed network as demonstrated in Fig. 1A. The users are the nodes in the network,and the re-postings are the edges in the network. And we the mark network creator using
color green. Each edge has a direction that is either from creator to re-poster or fromformer re-poster to later re-poster. We plot ﬁgures of typical networks for both fake andreal news of Weibo and Twitter as shown in Fig. 1B to 1E.
Ratio of layer sizes. The layer number is deﬁned as the number of hops from the creator
to a given re-poster. The ratio of layer sizes is a measure for each network deﬁned as:
ratio of layer sizes =

n2
,
n1

(1)

n1 and n2 are the sizes (number of nodes) of the ﬁrst and second layer for a certain
network respectively.
Characteristic distances. In order to measure the distances, for each network we ﬁrst
calculate the distances between all pairs of nodes in the network and plot the distribution
in a logarithmic scale (y axis). It can be seen from Fig. 4 that the function can be approximated by an exponential function. We consider the linear part of curves where their x
value (distance) is above one. We calculate the characteristic distance (a) accordingly:xy ∼ e– a +b .

(2)

Zhao et al. EPJ Data Science(2020) 9:7

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Heterogeneity measure. The heterogeneity [35] is deﬁned as:Heterogeneity =k 2 

k

 
N
1
=

N

2
i=1 ki1 N
i=1 kiN,(3)

N : The number of nodes in the network,
ki : The degree of node i.
We show a scatter plot (Fig. 5A) for both fake and real news of Weibo. The black line is
the theoretical line for star network:
Heterogeneous ∼

√

N.

(4)

The h is the diﬀerence between the logarithm of a real network heterogeneity value Hr andthe logarithm of heterogeneity value of the same-size star network Hs as shown below:
h = log(Hs ) – log(Hr ).

(5)

Probability of being fake news. Here we use the ratio of layer sizes as an example. We
divide the ratio of layer sizes into n portions. In the ith portion, the probability of being
fake news is:
f

p=

pi
f

pi + pri

,

(6)

f

pi : The probability of fake news in the ith portion (the number of fake news in thisportion divided by the total number of fake news).
pri : The probability of real news in the ith portion.
Signiﬁcance of diﬀerence. When we distinguish fake news from real ones using topological measures such as the ratio of layer sizes or the characteristic distance, it is important toknow the signiﬁcance of the diﬀerence. Here we use the ratio of layer sizes as an example.
First, we rank the Weibo propagation networks by their ratio of layer sizes ignoring theirtypes (fake or real). Second, we randomly split these propagation networks into n portions
that have the same number of networks. Finally, we calculate the diﬀerence signiﬁcanceusing the following formula:
1  max(pri , pi )
Q=
,
f
n 1
pri + pinfn: The number of portions that we divide.

Supplementary information
Supplementary information accompanies this paper at https://doi.org/10.1140/epjds/s13688-020-00224-z.
Additional ﬁle 1. Supplementary Information (DOCX 1.3 MB)(7)

Zhao et al. EPJ Data Science(2020) 9:7

Acknowledgements
SH thanks the Israel Science Foundation, ONR, the Israel Ministry of Science and Technology (MOST) with the Italy
Ministry of Foreign Aﬀairs, BSF-NSF, MOST with the Japan Science and Technology Agency, the BIU Center for Research in
Applied Cryptography and Cyber Security, and DTRA (Grant no. HDTRA-1-10-1-0014) for ﬁnancial support. JZ was
supported by NSFC (No. 71871006) and the National Key Research and Development Program of China(No. 2016QY01W0205). YS was supported by by JSPS KAKENHI Grand Number 17K12783. HT and MT are supported by JST
Strategic International Collaborative Research Program (SICORP) on the topic of “ICT for a Resilient Society” by Japan and
Israel. JW was partially supported by the National Key R&D Program of China (2019YFB2101804), the National Special
Program on Innovation Methodologies (SQ2019IM4910001), and the National Natural Science Foundation of China(71531001, 71725002, U1636210). We also thank Jiali Gao for providing new dataset of real news.
Funding
Not applicable.
Abbreviations
SVM, Support vector machine; RBF, Radial basis function (Gaussian) kernel; LCC, largest connected component.
Availability of data and materials
Our data is provided by author Jichang Zhao and will be available from him based on reasonable request.
Competing interests
The authors declare no competing interests.
Authors’ contributions
DL designed the research. ZZ, JZ, YS and OL contributed equally to this paper. ZZ and YS performed data calculation. OL,
ZZ, SH and DL wrote the paper. Other authors have analyzed the results and revised the paper. All authors read andapproved the ﬁnal manuscript.
Author details
1
School of Reliability and Systems Engineering, Beihang University, Beijing, China. 2 National Key Laboratory of Scienceand Technology on Reliability and Environmental Engineering, Beijing, China. 3 School of Economics and Management,
Beihang University, Beijing, China. 4 Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba,
Japan. 5 Department of Physics, Bar-Ilan University, Ramat Gan, Israel. 6 Sony Computer Science Laboratories, Tokyo,
Japan. 7 Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan. 8 Beijing Advanced Innovation
Center for Big Data and Brain Computing, Beihang University, Beijing, China.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional aﬃliations.
Received: 14 June 2019 Accepted: 25 February 2020
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