Content uploaded by Damian Frąszczak
Author content
All content in this area was uploaded by Damian Frąszczak on Feb 01, 2022
Content may be subject to copyright.
SoftwareX 17 (2022) 100988
Contents lists available at ScienceDirect
SoftwareX
journal homepage: www.elsevier.com/locate/softx
Original software publication
RPaSDT—Rumor Propagation and Source Detection Toolkit
Damian Frąszczak
Military University of Technology, ul. gen. Sylwestra Kaliskiego 2, 00-908 Warsaw, Poland
article info
Article history:
Received 24 August 2021
Received in revised form 12 December 2021
Accepted 11 January 2022
Keywords:
Python
Online social networks
Information propagation
Rumor source detection
abstract
Nowadays, online social networks are the primary method of communication between users around
the world. Unfortunately, they are increasingly used with malicious intent. Finding a rumor source is a
crucial attempt at controlling, preventing, and learning about the propagation of falsified information
in networks.
To alleviate this problem, RPaSDT (Rumor Propagation and Source Detection Toolkit) has been
developed to allow users to prepare and configure an initial network topology, a propagation process,
and then utilize the well-known source identification algorithms to estimate the authentic sources
based on the given diffusion graph.
The toolkit is designed to work in a window-based approach to display all performed analyses
simultaneously. It can also be used in other domains, e.g., identifying the influential nodes, simulating
the propagation of the epidemics in a society, or planning a marketing campaign to obtain the best
results.
©2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/).
Code metadata
Current code version 0.2.0
Permanent link to code/repository used of this code version https://github.com/ElsevierSoftwareX/SOFTX-D- 21-00167
Code Ocean compute capsule Not available because it is a GUI toolkit
Legal Code License MIT
Code versioning system used GIT
Software code languages, tools, and services used Python, Docker, PyInstaller, isort, typing
Compilation requirements, operating environments & dependencies Python, Docker, Referenced libraries: matplotlib, ndlib, network, PyQt5, cdlib,
numpy
If available Link to developer documentation/manual https://github.com/damianfraszczak/rpasdt/blob/main/README.md
Support email for questions damian.fraszczak@wat.edu.pl
Software metadata
Current software version 0.2.0
Permanent link to executables of this version https://github.com/damianfraszczak/rpasdt/tree/main/dist
Legal Software License MIT LICENCE
Computing platforms/Operating Systems iOS, Linux, Microsoft Windows
Installation requirements & dependencies Python, Docker, Referenced libraries: matplotlib, ndlib, network, PyQt5, cdlib,
numpy
If available, link to user manual - if formally published include a reference to
the publication in the reference list
https://github.com/damianfraszczak/rpasdt/blob/main/README.md
Support email for questions damian.fraszczak@wat.edu.pl
E-mail address: damian.fraszczak@wat.edu.pl.
1. Motivation and significance
Social media platforms provide an outstanding possibility to
share information inside a society, making our current world
https://doi.org/10.1016/j.softx.2022.100988
2352-7110/©2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
Damian Frąszczak SoftwareX 17 (2022) 100988
extremely compact and close. People use social media to share
information, emotions, and trends. Transferring information from
one person or the community to another in the network is known
as information diffusion or information propagation. The social
network structure characterized by no cost, great size, and instant
communication makes this process very convenient. The common
ways of information propagation like newspapers, TV, radio, etc.,
are becoming less popular.
Moreover, it is said that for most people, social media plat-
forms are the primary source of information, which exposes them
to very different types of information. There are many examples
of utilizing them with the right intention, like warning people
about dangerous situations or raising money for good causes.
Having mentioned properties of the social media platforms, they
also create an excellent opportunity to share information con-
taining malicious content. Recently, it has been observed that the
number of these incidents is increasing and can affect different
aspects of life, i.e., impacting the election results or both financial
and mental situations [1–3].
Identifying the source of malicious information is crucial as
it can reduce disinformation and consequently avoid more se-
vere problems. Furthermore, the issue of detecting the source
of the propagation of the network is critical in other cases, like
finding the patient zero in a disease. This can stop the spread
of the disease and control an epidemic. Another example is that
identifying a trojan virus or a computer worm in a network may
increase its effectiveness. Recently researchers have developed
a set of methods and techniques to solve this problem. The
presented solutions depend on the type of observation, network
topology, information diffusion process, etc. [3–5]. Unfortunately,
the proposed methods have not been combined into a common
framework, making it hard to analyze, use and compare with
others.
This paper aims to present RPaSDT software that helps to
overcome the problems mentioned above and aims to allow easy
and standardized access to a wide range of source identification
algorithms while making the processes of the analysis, evaluation,
visualization, and comparison easy. Moreover, it also provides a
set of functions that can be used in reverse problems: based on
the given network, find nodes from which propagation covers
the whole network in the shortest time. This problem is also
fundamental in epidemic management and preparing dedicated
marketing companies [6]. Some solutions provide similar func-
tionality to the presented software. [7–9] gives the options to
simulate propagation in the networks but with a restricted set
of diffusion models to those similar in an epidemic, Independent
Cascade, Threshold-based and available network topologies. This
toolkit extends propagation methods with dynamic opinion mod-
els and can be used in any network topology [4]. There are a
lot of dedicated tools for sophisticated network analysis available
in the market to [10–12] but without the possibility to simulate
and analyze the propagation and find sources based on it. No
open-source tool provides all of the mentioned functionalities and
allows utilizing the available functions with dedicated API or CLI.
To the best of the author’s knowledge, no solution provides the
implementation of the well-known algorithms for rumor source
detection in the given network.
Furthermore, there are no solutions that provide such ad-
vanced GUI and CLI layers that cover the process of propagation,
simulation, and source identification in the network in such a
complex way with a set of dedicated tools to analyze this. Both
layers utilize the shared API that other researchers can easily use
for their purpose. This solution aims to provide a starting point
for researchers to develop new source identification methods and
enable them to put their implementation here without the neces-
sity of knowing the auxiliary libraries. To sum up, the presented
toolkit allows researchers to prepare a propagation experiment
based on any network topology, including the actual network,
select and configure a diffusion model for information propaga-
tion from the selected sources in the network and utilize the
well-known source identification algorithms to estimate sourced
based on the diffusion network. Besides that, this toolkit comes
with a set of functionalities that can help with network analysis.
To conclude, all of this is packed into accessibility layers that
make the software easy to use with GUI and fast and valuable
for extensive networks with CLI.
2. Software description
The implemented toolkit allows the user to prepare a rumor
propagation experiment under any kind of network topology,
along with the well-known literature diffusion models, and, based
on the propagation graph, identify potential diffusion sources.
It is worth mentioning that the described toolkit provides a set
of auxiliary tools to perform sophisticated network analyses to
select different sources and verify how the diffusion under given
topology and sources set could behave. It is helpful to find an
optimal configuration to model, for example, an advertising cam-
paign and understand how the propagation looks with different
models, parameters, and network topologies. The software can
also simulate the propagation and source detection for other do-
mains like epidemics or virus detection. The propagation of these
can be simulated with available models in the toolkit and the
source identification process with available methods. The best to
author the knowledge about this is the first software that not only
allows it to simulate and visualize the information/epidemics etc.,
propagation but also to provide a complex set of well-known
algorithms used for the source detection in any type of network.
Moreover, it is the first open-source project that provides an
extensive source identification algorithm set of state-of-the-art
and well-known methods implemented.
2.1. Software architecture
The proposed application is based on Python [13] and a set of
great auxiliary graph-based libraries [14–16] to build an advanced
laboratory to simulate and analyze the information diffusion un-
der any kind of network topology and identify the source nodes
based on the propagation graph. Its architecture has been ori-
ented to provide a great set of interfaces easily used in both
GUI and CLI-based environments. As it is known, it is hard to
visualize an extensive network in GUI-based toolkits [6], so for
that case, the software provides the CLI layer that enables it to
perform all the operations without the UI. The architecture of
the implemented functionalities has been based on the Adapter
design pattern to combine different algorithms to get a result
under one command. The GUI layer has been implemented with
PyQT [17] that is a Python wrapper for C++ based QT UI libraries.
It means that the implemented software can be easily distributed
on any operating system. The GUI layer is built based on the
multi-window approach, which means each window provides a
different set of functionalities and contains a separate environ-
ment for the analysis (see Fig. 1). This approach allows users
to perform complex analyses on the different aspects simulta-
neously. Moreover, as each window has its context, the changes
in the current one do not affect the previous, and the next
created windows unless they are created on the current window
configuration.
The toolkit does not have any special requirements for the
hardware and services. It comes with dedicated installers for
both Windows and Linux users, making it easy to install and
use for non-technical persons. The development environment is
based on a Docker, so it is easy to run and extend the current
functionalities without installing and configuring any external
dependencies manually.
2
Damian Frąszczak SoftwareX 17 (2022) 100988
Fig. 1. RPaSDT—multi-window approach to visualize performed analysis.
Table 1
The summary of the window toolbars.
Graph visualization toolbar items They provide the following functionalities: back to the
initial view, undo or redo an operation, pan over the
network, zoom in and zoom out, edit subplots, figure
management, export current graph as an image, edit graph
rendering properties
Graph analysis toolbar items It allows you to perform any type of graph analysis with
centrality metrics, community detection, and network
properties.
Experiment toolbar items They provide the following functionalities: export the
current situation to be shared with other researchers,
select sources automatically with different algorithms,
navigate to the propagation step.
Propagation management toolbar items They provide propagation management functionalities like
edit diffusion model parameters, clear the propagation, run
a simulation in a step mode, run a simulation in a batch
mode, run a simulation to infect all nodes, choose and run
source detection.
2.2. Software functionalities
RPaSDT has been implemented in a window-based approach
to visualize and manage different aspects of the analysis. Each
window contains a separate model, which does not affect the
others. It means that the user can run multiple separate analyses
experiments on the initial network structure and compare them,
as is shown in the figure below. It is worth mentioning that users
can rearrange the windows in any way, which would make it
easier to analyze at the same time.
Each window has a separate toolbar that provides a different
set of operations to perform that can be divided into 2 main parts:
general features and case-specific features (see Table 1).
The implemented toolkit allows users to perform sophisticated
analyses of the propagation-based experiment with the following
steps:
1. Generate or load an initial network topology. A user can use
one of the ready-to-use network topologies, e.g., ‘‘Karate
club’’, generate a social network with well-known synthet-
ical models, or load a custom one based on a required
format.
2. Analyze the initial network structure with different graph-
based algorithms like centrality measures, community de-
tection, or network topology metrics.
3. Select propagation sources based on the analysis or auto-
matically with the provided algorithms, e.g., randomly or
based on centrality metrics.
4. Select, configure and run a propagation model under the
modeled situation. The simulation can be performed in
three different modes: step, batch, and whole. In this way,
a user can easily see how the situation is changed in each
step.
3
Damian Frąszczak SoftwareX 17 (2022) 100988
Fig. 2. Generated situation with performed degree centrality and community detection analysis.
5. Identify propagation sources based on the given diffusion
graph. This process can be performed in different time
moments, providing an excellent opportunity to under-
stand how the number of the infected nodes impacts the
accuracy of the source detection algorithms.
6. Verify the source detection accuracy.
3. Illustrative examples
RPaSDT is an intuitive software that directly leads a user from
the beginning to the end of the analysis process. The best way
to confirm that thesis is to show how to prepare and conduct an
experiment with the following requirements:
•A Watts–Strogatz synthetical graph will be used as a net-
work topology.
•The network will be analyzed under different aspects and
metrics.
•The source nodes will be selected based on their centrality
metrics.
•The rumor diffusion process with the SI model will be sim-
ulated with 6 iterations.
•The diffusion network will be analyzed under different as-
pects and metrics.
•Based on the diffusion graph, the source nodes will be
estimated based on some source identification methods (see
Fig. 2).
In the first step, a user is obligated to create or import an
already created experiment. To create a new experiment, the user
has to provide some basic information about it: i.e., name and
the graph type, and then the user has to provide a graph type
configuration. The config parameters depend on the type of the
graph. Currently, the user can choose from one of the following
options:
•Generate a synthetical graph: Watts–Strogatz, Erdős–Rényi,
Caveman, balanced tree, complete, star, etc.
•Use some typical graph topology like: ‘‘Karate club’’, ‘‘Davis
Southern women social network’’ or ‘‘Florentine families’’.
•Load a custom graph topology based on: an adjacency ma-
trix, GML, or JSON formats.
In the next step, the user can carry out an analysis of the graph
topology. The software provides a way to analyze the importance
of the nodes with the centrality measures, find communities
based on different algorithms and analyze the situation on the
graph level.
In the next step, the user is obligated to select sources for
propagation simulation. It can be done automatically or on the
performed analysis. By default, selected nodes are marked with a
red color, but they can be changed with user settings.
Afterward, the user has to choose and configure a diffusion
model to be used to simulate propagation over the network.
When it is ready, the propagation management window will
pop up. The number of sources is not imposed. When the initial
situation is fully configured, the user should set up a propagation
experiment. The toolkit allows modeling to process various ap-
proaches like epidemic models, social influence models, e.g., Inde-
pendent Cascade Models or Threshold-based models, and opinion
dynamics models. The wide range of the available propagation
models allows the user to simulate and verify different scenarios
and aspects under the given network topology.
After configuring the propagation model with its parameters,
the diffusion experiment is ready to start. As mentioned in the
previous section, the propagation window brings a propagation
management toolbar that allows managing the simulation pro-
cess. It can be run in three different modes: step, batch, and full
network infection. This functionality allows the user to monitor
and understand how the selected propagation model will work
under different network topologies with the given set of sources
and how it will proceed. To this point, the software can also be
used for other domains like epidemic simulations in a particular
society, the advertisement campaign prediction for the given
product under a particular group of users, or the prediction of the
propagation for a computer virus infection in an internal network
and the possible consequences of that (see Fig. 3).
It is worth mentioning that with the utilized window-based
approach to building UI, the researchers can graphically compare
4
Damian Frąszczak SoftwareX 17 (2022) 100988
Fig. 3. The results of the rumor propagation simulation are visible along with other windows.
Fig. 4. The results of the rumor source detection process.
how the different diffusion models will cover the network simul-
taneously. It is beneficial to analyze the propagation in this way. It
allows them to find out crucial things about this, e.g., with what
model the most critical nodes will take part in the propagation
the fastest or what model will provide the best coverage of the
nodes under restricted time.
The last step in the experiment is to carry out a source identi-
fication process based on the provided propagation graph. The re-
sults of the selected algorithm are displayed in two ways: via the
graph where a yellow color marks the estimated sources nodes.
Moreover, on other tabs of the source detection toolkit, there are
displayed the most popular classification metrics used in a task of
source detection like accuracy, recall, precision, f-measure, or dis-
tance error between actual and incorrectly detected nodes [4,18]
but also provides a set of well-known classification metrics [19]
and a confusion matrix visualization (see Fig. 4).
The utilization of the multi-window approach for UI pro-
vides another excellent opportunity to compare different source
identification methods at the same time under different condi-
tions, e.g., the different network coverage, propagation model, or
authentic sources set (see Fig. 5).
4. Impact
The presented toolkit provides an extensive set of tools that
allows the user to quickly and easily create experimental sce-
narios or import real ones to study the propagation and find
propagation sources in the networks. This software utilizes the
set of already existing libraries to build, analyze and visualize
networks in the Python language and provides an additional layer
to make it easier for the researchers to use them. In general, these
functionalities can be achieved easily by researchers’ scripts in a
not so interactive manner. The presented toolkit comes with both
UI and CLI interfaces to overcome that problem.
The UI layer was implemented according to the multi-window
approach that allows researchers to see different network analy-
ses and, at the same time, which makes it easier to understand a
problem and find a potential solution.
The software can also easily be used to analyze, simulate
the propagation, and perform source detection in other domains
like epidemics, virus detection, or advertising campaigns as the
propagation of these can be simulated with available models in
the toolkit and the source identification process can be performed
with the available methods. The presented software comes with
5
Damian Frąszczak SoftwareX 17 (2022) 100988
Fig. 5. The rumor source identification accuracy for different algorithms at the same time via network rendering.
documentation available online [20] that provides usage exam-
ples with GUI, CLI, and API to perform sophisticated analysis and
consist of instructions to run and configure applications from
scratch.
To the best of the author’s knowledge, this is the first soft-
ware program that allows the user to simulate and visualize
the information/epidemics, etc., propagation and provide a com-
plex set of well-known algorithms used for the source detec-
tion in any type of network. Currently, the toolkit provides an
implementation for both the single and multi-source detection
problems. Single sources can be detected with: NetSleuth [20],
DynamicAge [21], RumorCenter [22–24], JordanCenter [25] and
centrality-based methods [26,27]. Multiple sources can be de-
tected with mentioned techniques utilizing more than 20 com-
munity detection and network partitioning methods to transform
the multi-source detection problem into several independent sin-
gle source-locating problems [28–30] and centrality-based meth-
ods [26,27]. There are still many other methods to detect a
rumor source [3,18,31], but the ones mentioned above are most
cited in the literature. The toolkit’s introduction gives the great
opportunity to create a common and shared place to test and de-
velop new source detection methods that are crucial in reducing
disinformation and consequently avoid more severe problems in
the future.
5. Conclusions
RPaSDT is a state-of-the-art toolkit providing a set of function-
alities to help researchers perform sophisticated network analy-
ses, simulate information propagation, and identify the diffusion
sources with well-known methods. The software’s primary pur-
pose is to analyze social networks and identify the rumor’s source
but can be easily adapted and used in other propagation-based
domains like epidemics, advertising, or network security. What
is also essential is that the toolkit comes with the CLI layer
that allows analyzing the extensive networks with the provided
algorithms.
The presented software can be extended in many areas like
providing a new set of network analysis methods, providing the
possibility to import the network structure from the internet’s so-
cial network, e.g., build a network based on a tweet or implement
the other source identification methods. RPaSDT is still under
development as it is part of the author’s Ph.D. thesis regarding
the preparation of a new method to identify the source of fake
news in online social networks. Moreover, this thesis also focuses
on information propagation data fusion from different social net-
works to provide a more complex situation for source detection
methods.
To the best of the author’s knowledge, this is the first solution
that covers the network propagation problem in such a complex
way, and it is the first open-source solution that contains the set
of well-known source identification algorithms implemented.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared
to influence the work reported in this paper.
References
[1] Higdon N. The anatomy of fake news: a critical news literacy education.
Oakland, California: University of California Press; 2020.
[2] Meel P, Vishwakarma DK. ‘Fake news, rumor, information pollution in so-
cial media and web: A contemporary survey of state-of-the-arts, challenges
and opportunities’. Expert Syst Appl 2020;153:112986. http://dx.doi.org/10.
1016/j.eswa.2019.112986.
[3] Frąszczak D. ‘Fake news source detection – the state of the art survey for
current problems and research’. In: Proceedings of the 37th international
business information management association. Cordoba, Spain; 2021, p.
11381–9. http://dx.doi.org/10.6084/m9.figshare.16545675.
[4] Frąszczak D. Information Propagation In Online Social Networks - A
Simulation Case Study. In: Proceedings of the 38th international business
information management association. Seville, Spain; 2021, https://doi.org/
10.6084/m9.figshare.18974987.v1.
[5] Jin R, Wu W. ‘Schemes of propagation models and source estimators
for rumor source detection in online social networks: A short survey
of a decade of research’. 2021, ArXiv210100753 Cs, [Online]. Available:
http://arxiv.org/abs/2101.00753 [Accessed: 13 March 2021].
[6] K. Raj PM, Mohan A, Srinivasa KG. Practical social network analysis with
python. Cham: Springer International Publishing; 2018, http://dx.doi.org/
10.1007/978-3- 319-96746- 2.
[7] Karczmarczyk A, Jankowski J, Wątróbski J. ‘OONIS — Object-oriented
network infection simulator’. SoftwareX 2021;14:100675. http://dx.doi.org/
10.1016/j.softx.2021.100675.
6
Damian Frąszczak SoftwareX 17 (2022) 100988
[8] Witten G, Poulter G. ‘Simulations of infectious diseases on net-
works’. Comput Biol Med 2007;37(2):195–205. http://dx.doi.org/10.1016/
j.compbiomed.2005.12.002.
[9] Vallet J, Kirchner H, Pinaud B, Melançon G. ‘A visual analytics approach
to compare propagation models in social networks’. Electron Proc Theor
Comput Sci 2015;181:65–79. http://dx.doi.org/10.4204/EPTCS.181.5.
[10] Otasek D, Morris JH, Bouças J, Pico AR, Demchak B. ‘Cytoscape au-
tomation: empowering workflow-based network analysis’. Genome Biol
2019;20(1):185. http://dx.doi.org/10.1186/s13059-019- 1758-4.
[11] Gephi. - The open graph viz platform’. 2021, https://gephi.org/ [Accessed
11 August 2021].
[12] Graph-tool: Efficent network analysis with python’. 2021, https://graph-
tool.skewed.de/ [Accessed 24 August 2021].
[13] ‘Welcome to python.org’. 2021, https://www.python.org/ [Accessed 11
August 2021].
[14] Rossetti G, Milli L, Cazabet R. ‘CDLIB: A python library to extract, com-
pare and evaluate communities from complex networks’. Appl Netw Sci
2019;4(1):52. http://dx.doi.org/10.1007/s41109-019- 0165-9.
[15] Rossetti G, Milli L, Rinzivillo S, Sîrbu A, Pedreschi D, Giannotti F. ‘Ndlib:
a python library to model and analyze diffusion processes over complex
networks’. Int J Data Sci Anal 2018;5(1):61–79. http://dx.doi.org/10.1007/
s41060-017- 0086-6.
[16] ‘Networkx — Networkx documentation’. 2021, https://networkx.org/
[Accessed 11 August 2021].
[17] ‘Qt for Python — Qt for Python’. 2021, https://doc.qt.io/qtforpython/
[Accessed 11 August 2021].
[18] Shelke S, Attar V. ‘Source detection of rumor in social network – a review’.
Online Soc Netw Media 2019;9:30–42. http://dx.doi.org/10.1016/j.osnem.
2018.12.001.
[19] Harrison M. Machine learning pocket reference: working with structured
data in python, first edition. Beijing ; Boston: O’Reilly; 2019.
[20] Prakash BA, Vreeken J, Faloutsos C. ‘Spotting culprits in epidemics: How
many and which ones?’. In: 2012 IEEE 12th international conference on
data mining. Brussels, Belgium; 2012, p. 11–20. http://dx.doi.org/10.1109/
ICDM.2012.136.
[21] Fioriti V, Chinnici M. ‘Predicting the sources of an outbreak with a spec-
tral technique’. 2012, ArXiv12112333 Math-Ph Physicsphysics, [Online].
Available: http://arxiv.org/abs/1211.2333 [Accessed: 06 May 2021].
[22] Shah D, Zaman T. ‘Rumors in a network: Who’s the culprit?’. IEEE
Trans Inform Theory 2011;57(8):5163–81. http://dx.doi.org/10.1109/TIT.
2011.2158885.
[23] Shah D, Zaman T. ‘Detecting sources of computer viruses in networks: the-
ory and experiment’. In: Proceedings of the ACM sigmetrics international
conference on measurement and modeling of computer systems. New
York, New York, USA; 2010, p. 203. http://dx.doi.org/10.1145/1811039.
1811063.
[24] Dong W, Zhang W, Tan CW. ‘Rooting out the rumor culprit from suspects’.
In: IEEE int symp inf theory. 2013, p. 2671–5. http://dx.doi.org/10.1109/
ISIT.2013.6620711.
[25] Zhu K, Ying L. Information source detection in the SIR model: A sample
path based approach’. 2013, ArXiv12065421 Phys., [Online]. Available:
http://arxiv.org/abs/1206.5421 [Accessed: 13 March 2021].
[26] Das K, Kumar Sinha S. ‘Centrality measure based approach for detec-
tion of malicious nodes in twitter social network’. Int J Eng Technol
2018;7(4.5):518. http://dx.doi.org/10.14419/ijet.v7i4.5.21147.
[27] Ali SS, Anwar T, Rizvi SAM. ‘A revisit to the infection source identification
problem under classical graph centrality measures’. Online Soc Netw Media
2020;17:100061. http://dx.doi.org/10.1016/j.osnem.2020.100061.
[28] Luo W, Tay WP. ‘Identifying multiple infection sources in a network’. In:
2012 conference record of the forty sixth asilomar conference on signals.
Systems and computers (ASILOMAR), Pacific Grove, CA, USA; 2012, p.
1483–9. http://dx.doi.org/10.1109/ACSSC.2012.6489274.
[29] Zang W, Zhang P, Zhou C, Guo L. ‘Discovering multiple diffusion source
nodes in social networks’. Procedia Comput Sci 2014;29:443–52. http:
//dx.doi.org/10.1016/j.procs.2014.05.040.
[30] Zang W, Zhang P, Zhou C, Guo L. ‘Locating multiple sources in social
networks under the SIR model: A divide-and-conquer approach’. J Comput
Sci 2015;10:278–87. http://dx.doi.org/10.1016/j.jocs.2015.05.002.
[31] Jiang J, Wen S, Yu S, Xiang Y, Zhou W. ‘Identifying propagation sources in
networks: State-of-the-art and comparative studies’. IEEE Commun Surv
Tutor 2017;19(1):465–81. http://dx.doi.org/10.1109/COMST.2016.2615098.
7