Identifying spreading influence nodes for social networks

doi:10.1007/s42524-022-0190-8

Front. Eng

2022, Vol. 9

Issue (4) : 520-549 https://doi.org/10.1007/s42524-022-0190-8

REVIEW ARTICLE

Identifying spreading influence nodes for social networks

Yang OU¹, Qiang GUO¹, Jianguo LIU²(

)

¹. Research Center of Complex Systems Science, University of Shanghai for Science and Technology, Shanghai 200093, China
². Institute of Accounting and Finance, Shanghai University of Finance and Economics, Shanghai 200433, China

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Abstract

The identification of spreading influence nodes in social networks, which studies how to detect important individuals in human society, has attracted increasing attention from physical and computer science, social science and economics communities. The identification algorithms of spreading influence nodes can be used to evaluate the spreading influence, describe the node’s position, and identify interaction centralities. This review summarizes the recent progress about the identification algorithms of spreading influence nodes from the viewpoint of social networks, emphasizing the contributions from physical perspectives and approaches, including the microstructure-based algorithms, community structure-based algorithms, macrostructure-based algorithms, and machine learning-based algorithms. We introduce diffusion models and performance evaluation metrics, and outline future challenges of the identification of spreading influence nodes.

Keywords complex network network science spreading influence machine learning

Corresponding Author(s): Jianguo LIU

Just Accepted Date: 16 May 2022 Online First Date: 01 September 2022 Issue Date: 08 December 2022

Cite this article:

Yang OU,Qiang GUO,Jianguo LIU. Identifying spreading influence nodes for social networks[J]. Front. Eng, 2022, 9(4): 520-549.

URL:

https://academic.hep.com.cn/fem/EN/10.1007/s42524-022-0190-8
https://academic.hep.com.cn/fem/EN/Y2022/V9/I4/520

Approach	Category	Study problem	Data	Diffusion model	Main analysis findings
Percolation-based greedy algorithm (PBGA) (Hu et al., 2018)	MSB	Influence maximization	GrQc (Leskovec et al., 2007), HepTh (Leskovec et al., 2007), Enron (Leskovec et al., 2009), NoLA Facebook, DBLP (Yang and Leskovec, 2012), QQ (Ren et al., 2015), LiveJournal (Yang and Leskovec, 2012), Weibo, Delicious (Lü et al., 2011)	Susceptible-infected-recovered (SIR) (Hethcote, 2000)	The spreading influence of nodes can be approximately estimated by using the local structural information of nodes
Spreading strength (SS) (Yu et al., 2019)		Node ranking	Facebook (McAuley and Leskovec, 2012), PGP (Bogu?á et al., 2004), Protein (Jeong et al., 2001), Guntella08 (Leskovec et al., 2007), GrQc (Leskovec et al., 2007), CondMat (Leskovec et al., 2007), HepTh (Leskovec et al., 2007), US Air, PowerGrid (Watts and Strogatz, 1998)	SIR (Hethcote, 2000)	The indirect influence of a node on its neighborhood is important for measuring the spreading influence of the node
Local centrality (LC) (Chen et al., 2012)		Node ranking	Blog (Xie, 2006), Netscience (Newman, 2006), Router (Spring et al., 2002), Email (Guimerà et al., 2003)	SIR (Hethcote, 2000)	The degree information of high-order neighbors can improve the accuracy and resolution of the degree centrality (DC)
Neighborhood centrality (NC) (Liu et al., 2016b)		Node ranking	Email (Guimerà et al., 2003), HepTh (Leskovec et al., 2007), Hamster (Kunegis, 2016), PGP (Bogu?á et al., 2004), Astro Physics (Newman, 2001), Router (Spring et al., 2002)	SIR (Hethcote, 2000)	Considering the structural information of a node’s neighbors within two steps is a good choice to balance accuracy and efficiency
Local structure similarity (LSS) (Liu et al., 2017a)		Influence maximization	GrQc (Leskovec et al., 2007), Router (Spring et al., 2002), Hamster (Kunegis, 2016), Polblogs	SIR (Hethcote, 2000), Susceptible-infected (SI) (Barabási and Albert, 1999)	The local structural property of nodes can help identify multiple spreading influence nodes more accurately than by using the distance
VoteRank (Zhang et al., 2016)		Influence maximization	YouTube (Yang and Leskovec, 2012), CondMat (Leskovec et al., 2007), Berkstan (Leskovec et al., 2009), Notre DAME (Albert et al., 1999)	SIR (Hethcote, 2000), SI (Barabási and Albert, 1999)	The performance of VoteRank is highly correlated with the number of ranked nodes
ClusterRank (CR) (Chen et al., 2013)		Node ranking	Delicious (Lü et al., 2011), SM	SIR (Hethcote, 2000)	Nodes with small clustering coefficients are likely to connect with more nodes in the future
Local structure centrality (LSC) (Gao et al., 2014)		Node ranking	Email (Guimerà et al., 2003), Blog, PGP (Bogu?á et al., 2004), Twitter	SIR (Hethcote, 2000)	The positive effect of the clustering coefficient of a node’s second-order neighbors has a significant influence on the spreading influence of the node
V-communities (Vc) (Zhao et al., 2014b)	CSB	Node ranking	Facebook (McAuley and Leskovec, 2012), GrQc (Leskovec et al., 2007), Netscience (Newman, 2006), Protein (Jeong et al., 2001)	SIR (Hethcote, 2000)	The number of communities connected to a node can help detect the spreading influence nodes that a single centrality may ignore
Community-based centrality (CbC) (Zhao et al., 2015)		Node ranking	Facebook (McAuley and Leskovec, 2012), Metabolic, Email, PowerGrid (Watts and Strogatz, 1998), Router (Spring et al., 2002), Blogcatalog	SIR (Hethcote, 2000)	The size of the community and the distribution of a node’s neighbors in each community play important roles in measuring the node’s spreading influence
Community-based mediator (CbM) (Tulu et al., 2018)		Node ranking	Karate (Zachary, 1977), American football network (Girvan and Newman, 2002), Dolphin (Lusseau et al., 2003), Airport, Internet	SIR (Hethcote, 2000)	The edge density within each community and the edge density between communities can be used to identify spreading influence nodes accurately with low computational complexity
Community-hole index (CHR) (Wang et al., 2018)		Node ranking	GrQc (Leskovec et al., 2007), Weibo (Tang and Liu, 2009), arXiv (Pan and Saram?ki, 2012), Amazon	SIR (Hethcote, 2000)	The importance of communities connected to a node is related to the node’s spreading influence
Modular centrality (MC) (Ghalmane et al., 2019a)		Node ranking	Facebook (McAuley and Leskovec, 2012), Netscience (Newman, 2006), GrQc (Leskovec et al., 2007)	SIR (Hethcote, 2000)	Dividing the network with an overlapping community structure into local and global networks can help identify spreading influence nodes more accurately
Network global structure-based centrality (NGSC) (Namtirtha et al., 2021)	MASB	Influence maximization	Odlis, Netscience (Newman, 2006), Advogato (Massa et al., 2009)	SIR (Hethcote, 2000)	The network components and network density have a significant influence on the performance of identification algorithms
Gravity centrality (GC) (Ma et al., 2016)		Node ranking	Facebook, Netscience (Newman, 2006), Email (Guimerà et al., 2003), TAP (Zeng and Zhang, 2013), Y2H (Kumar and Snyder, 2002), Blogs (Xie, 2006), Router (Spring et al., 2002), HepTh (Leskovec et al., 2007), PGP (Bogu?á et al., 2004)	SIR (Hethcote, 2000)	The gravity model can be applied to identify the spreading influence of nodes with relatively high accuracy
$C EffG$ (Shang et al., 2021)		Node ranking	Jazz, Netscience (Newman, 2006), GrQc (Leskovec et al., 2007), EEC, Email, PB, Facebook, US Air, Physicians, PDZBase, Haggle, Infectious	SI (Barabási and Albert, 1999)	Replacing the Euclidean distance of the gravity model by the effective distance can achieve higher accuracy
Dynamic-sensitive (DS) (Liu et al., 2016a)		Influence maximization	Erdos, Email contact (Kitsak et al., 2010), Router (Spring et al., 2002), Protein (Jeong et al., 2001)	SIR (Hethcote, 2000), SI (Barabási and Albert, 1999)	The spreading influence of a node is determined by topological structures and the spreading dynamics
Influence capacity (Wang et al., 2016)		Node ranking	Karate (Zachary, 1977), Netscience (Newman, 2006), Dolphin (Lusseau et al., 2003), Email (Guimerà et al., 2003), Jazz, PGP (Bogu?á et al., 2004), Blog (Xie, 2006), Facebook, Enron (Leskovec et al., 2009), Twitter	SIR (Hethcote, 2000)	The order in which nodes within the same layer are removed can distinguish the spreading influence of nodes located in the same shell
Link entropy (Liu et al., 2015a)		Node ranking	Router (Spring et al., 2002), Email contact (Kitsak et al., 2010), AS, Email (Guimerà et al., 2003), HepTh (Leskovec et al., 2007), Hamster (Kunegis, 2016), PGP (Bogu?á et al., 2004), Netscience (Newman, 2006), Astro Physics (Newman, 2001)	SIR (Hethcote, 2000)	The node with high coreness is a spreading influence node with a strong edge diversity to nodes located in other shells of the network
$θ$ (Liu et al., 2013a)		Node ranking	Email (Guimerà et al., 2003), PGP (Bogu?á et al., 2004), AS, P2P (Leskovec et al., 2007)	SIR (Hethcote, 2000)	The distance from the node to nodes in the core–shell layer can effectively distinguish the spreading influence of nodes in the same shell layer
Multicentrality predictors (Bucur, 2020)	MLB	Node ranking	Adolescent, Advogato (Massa et al., 2009), Astro Physics (Newman, 2001), CondMat (Leskovec et al., 2007), GrQc (Leskovec et al., 2007), HepTh (Leskovec et al., 2007), AS, Brightkite, Email, Epinions, Euroroad, Facebook, Github, Guntella, Googleplus, Hamster (Kunegis, 2016), IMDB, OpenFlights, PGP (Bogu?á et al., 2004), Twitch, Twitter Stanford, US Airports, PowerGrid (Watts and Strogatz, 1998), WikiTalk	SIR (Hethcote, 2000)	The spreading influence nodes identified by the MSB algorithms may be located in the peripheral regions of the network, and the MASB algorithms can help to rectify this shortcoming
Perturb and combine (P&C) (Tixier et al., 2019)		Node ranking	Email (Klimt and Yang, 2004), Epinions, WikiVote	SIR (Hethcote, 2000)	The idea of ensemble learning can improve the robustness of the $k$ -core and PageRank algorithm
Influence deep learning (IDL) (Wang et al., 2019)		Node ranking	Sina Weibo, Epinions, WikiVote, NetHEPT (Pal et al., 2014)	Independent cascading (IC) (Kempe et al., 2003)	The graph convolutional networking (GCN) model has a great potential for the identification of spreading influence nodes

Tab.1 Approach names, categories, study problems, data, diffusion models, and main analysis findings of the representative MSB, CSB, MASB, and MLB algorithms

Fig.1 Diagram of four types of networks: (a) undirected and unweighted network; (b) directed and unweighted network; (c) undirected and weighted network; and (d) directed and weighted network.

Fig.2 Diagram of nodes with the same number of first-order neighbors but a different number of second-order neighbors.

Methods	Advantages	Disadvantages	Computational complexity
DC (Freeman, 1978)	Low computational complexity; Simple and easy to understand	The structure information of high-order neighbors is ignored	$O (n)$
LC (Chen et al., 2012)	Considers the degree of high-order neighbor nodes	Other structural attributes are disregarded, except the degree of the node	$O (? k ? n 2)$
LNC (Dai et al., 2019)	Measures the contributions of different neighbors to the spreading influence of the node; Outperforms DC and betweenness while keeping low computational complexity	Unsuitable for the random network	$O (? k ? n)$
VoteRank (Zhang et al., 2016)	Uses the idea of voting to aggregate the structural information of high-order neighbors; The accuracy is higher than PageRank and LeaderRank; Low computational complexity	The differences in the initial voting abilities of nodes are ignored	$O (n)$
AIRank (Zhang et al., 2019b)	Distinguishes the voting abilities of nodes from the perspective of individuals and groups	The performance will be unstable when the edge density between communities is low	$O (n)$
NCRank (Kumar and Panda, 2020)	Distinguishes the voting abilities of nodes by considering the position of the node	Adjusting free parameters to obtain a stable performance is time consuming	$O (n)$
EnRenew (Guo et al., 2020)	Different initial voting abilities of nodes are distinguished on the basis of the information entropy	The computational complexity is higher than VoteRank	$O (m + n + r log ? (n) + m 2 n 2)$
DynamicRank (Chen et al., 2019)	Uses the probabilities of high-order neighbors being influenced to measure the spreading influence of nodes	Adjusting the free parameter to obtain a stable performance is time consuming	$O (n)$

Tab.2 Advantages and disadvantages of representative MSB algorithms, where

r

is the total number of iteration rounds,

? k ?

is the average degree of nodes, and

n

and

m

are total number of nodes and edges of a network, respectively

Tab.3 Advantages and disadvantages of five main MSB method streams

Fig.3 Diagram of local and global network division of the network with overlapping community structure.

Methods	Advantages	Disadvantages	Computational complexity
Vc (Zhao et al., 2014b)	Identifies spreading influence nodes that cannot be detected by a single centrality	The performance will be unstable when the community structure of the network changes	$O (n)$
CbC (Zhao et al., 2015)	Alleviates the instability of Vc by considering the community size and the distribution of neighbors	Other community structural attributes are not used except the size of the community	$O (n ? k ?)$
CbM (Tulu et al., 2018)	The edge densities within and between communities are considered; CbM outperforms CbC	The computational complexity is higher than CbC	$O (m n ? k ?)$
CGA (Wang et al., 2010)	Reduces the computational complexity of MixGreedy by narrowing the searching space to the community scale	The accuracy is lower than MixGreedy	$O (M K T p + K N C o m p T p)$
Community-based framework for influence maximization (CoFIM) (Shang et al., 2017)	Divides the propagation process into two phases, which is more explainable; The computational complexity is low while keeping high accuracy	Determining an appropriate infection rate and free parameters is time consuming	$O (K 2 n k max)$
PHG (Qiu et al., 2019)	Reduces the computational complexity by filtering candidates before applying the greedy algorithm	Only considers the degree of nodes when identifying the core node set	$O (n l o g n + n + K n ′ m ′)$
ICC (Zhao et al., 2020c)	Improves the performance of CC by adopting community structural attributes	Unsuitable for large-scale networks	–
Community-based influence maximization (CIM) (Chen et al., 2014)	Narrows the seed nodes’ searching space by the size of the community	Other community structural attributes are ignored, except the size of the community	–
CHR (Wang et al., 2018)	Considers the influence of community-level importance to node-level importance	Unsuitable for large-scale networks	–

Tab.4 Advantages and disadvantages of representative CSB algorithms, where

K

is the number of seed nodes,

M

is the total number of communities,

T p

is the time to compute the degree of a node in community

p

N C o m p

is the size of community

p

, and

n ′

and

m ′

are the number of candidate nodes and edges, respectively

Tab.5 Advantages and disadvantages of three main CSB method streams

Fig.4 Diagram of

k

-shell decomposition: (a) original network; (b) network after the first removal of nodes with degree 1; and (c) network after all nodes with degree 1 have been removed.

Fig.5 Diagram of the structural hole (adapted from Su and Song (2015)): (a) network with a structural hole; and (b) network without a structural hole.

Methods	Advantages	Disadvantages	Computational complexity
BC (Freeman, 1977)	Identifies nodes that have strong control over the spreading process	High computational complexity; Unsuitable for large-scale networks	$O (n 3)$
CC (Sabidussi, 1966)	Uses the distances between nodes to measure the spreading of nodes	High computational complexity; Unsuitable for large-scale networks	$O (n 3)$
PageRank (Brin and Page, 1998)	Aggregates the structure information of neighbor nodes iteratively; Low computational complexity	Difficult to converge when there are nodes with an out-degree 0	$O (m)$
$k$ -shell (Kitsak et al., 2010)	Considers the position of the node on the basis of the node’s degree	The spreading influence of nodes in the same shell layer cannot be distinguished	$O (n)$
LeaderRank (Lü et al., 2011)	Ensures a faster convergence speed than PageRank by adding a ground node	Only suitable for directed networks	$O (m)$
Local and global node influence (LGI) (Ma et al., 2020)	Introduces the entropy to distinguish differences in the spreading influence of nodes in the same shell layer	Tuning free parameters is time consuming	$O (n 2 + m)$
CumulativeRank (Zhang et al., 2019a)	The local and global spreading influence of nodes is considered simultaneously	Unsuitable for random networks	$O (n 2 + n ? k ? 2)$
GSM (Ullah et al., 2021)	Considers the self-importance of the node and the relationship of the node with other nodes simultaneously	High computational complexity; Unsuitable for large-scale networks	$O (n 2)$
IKs (Liu et al., 2015b)	The nodes are divided into different shell layers in a more granular manner	Unsuitable for random networks	$O (n)$

Tab.6 Advantages and disadvantages of representative MASB algorithms

Method streams	Related works	Advantages	Disadvantages
Iteration-based	EC (Bonacich, 1972); PageRank (Brin and Page, 1998); LeaderRank (Lü et al., 2011); WleaderRank (Li et al., 2014)	Aggregates the structural information of neighbor nodes in an iterative manner, which is more efficient than directly exploiting the structural information of the entire network	The contribution of neighbor nodes to the spreading influence of the target node is mainly measured by the degree information
$k$ -shell-based	$θ$ (Liu et al., 2013a); Resource Allocation Dynamics (Ma et al., 2014); IKs (Liu et al., 2015b); DSC (Zareie et al., 2019); $C nc$ (Bae and Kim, 2014); Link entropy (Liu et al., 2015a); Influence capacity (Wang et al., 2016); Classified neighbors (CN) (Li et al., 2018)	The position information of nodes in the network is considered, which can avoid to identify nodes located in peripheral regions of the network as spreading influence nodes	The nodes located in the core–shell layer are not always the spreading influence nodes
Micro-macro-based	NGSC (Namtirtha et al., 2021); ksd (Maji, 2020); Influence (Ma et al., 2020)	Guarantees stable performance in both sparsely and densely connected networks	Weights assigned to each attribute need to be predefined, which is time consuming
Gravity-model-based	GC (Ma et al., 2016); GM (Li et al., 2019); Yan et al. (2020); $C EffG$ (Shang et al., 2021); Effective distance gravity model (EDGM) (Chen et al., 2021b)	Considers the position of nodes and the effect of the distance between nodes on their interaction	The calculation of distance results in high computational complexity

Tab.7 Advantages and disadvantages of four main MASB method streams

Fig.6 Framework of IDL (adapted from Wang et al. (2019)).

Fig.7 Framework of RCNN.

Fig.8 Simplified architecture of the ConvGNN-based algorithms.

Tab.8 Advantages and disadvantages of representative MLB algorithms

Tab.9 Advantages and disadvantages of two main MLB method streams

Tab.10 Advantages and disadvantages of MSB, CSB, MASB, and MLB algorithms

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