WO2017023322A1

WO2017023322A1 - Influence spread maximization in social networks

Info

Publication number: WO2017023322A1
Application number: PCT/US2015/043932
Authority: WO
Inventors: Han JU; Lakshmi Nagarajan; Shi Xing Yan
Original assignee: Hewlett Packard Enterprise Development Lp
Priority date: 2015-08-06
Filing date: 2015-08-06
Publication date: 2017-02-09

Abstract

The present subject matter relates to maximizing spread of influence in social networks. In an example implementation, a benefit of selection value for each node in a social network is computed. A node is selected into a set of nodes, for which the benefit of selection value is maximum. The benefit of selection value of each immediate successor node of the selected node is reduced by a factor of one minus the degree of influence of the selected node on a respective immediate successor node of the selected node. The benefit of selection value of each immediate predecessor node of the selected node is reduced at least by a value of the degree of influence of a respective immediate predecessor node on the selected node. A next node from remaining nodes for which the benefit of selection value is maximum is selected into the set of nodes.

Description

INFLUENCE SPREAD MAXIMIZATION IN SOCIAL NETWORKS BACKGROUND

[0001] Social networks, such as online social media networks or telecommunication networks, include network users that may communicate with each other to share content or information. The network users receiving the content may get influenced by the received content. One or more of the network users may further share the received content with their peer network users to influence the peer network users. The social networks are generally analyzed to identify a set of network users that have a maximum spread of influence amongst the network users. The set of network users identified based on the analysis can be utilized to disseminate and discover useful and novel content across the network users, and also to monitor the flow of information in the social network. BRIEF DESCRIPTION OF DRAWINGS

[0002] The following detailed description references the drawings, wherein:

[0003] Fig.1 illustrates an influence spread maximizing system, according to an example implementation of the present subject matter;

[0004] Fig. 2 illustrates a network topology, according to an example implementation of the present subject matter;

[0005] Fig. 3 illustrates an example network environment implementing the influence spread maximizing system, according to an example implementation of the present subject matter;

[0006] Fig. 4 illustrates a method for determining a set of nodes that has a maximum spread of influence with a social network, according to an example implementation of the present subject matter; and

[0007] Fig.5 illustrates an example network environment for determining a set of nodes that has a maximum spread of influence with a social network, according to an example implementation of the present subject matter. DETAILED DESCRIPTION

[0008] For the purpose of social network analysis, a social network may be modelled to create a network topology of network users and influential relationships between the network users in the social network. The network users are represented as nodes in the network topology. The influential relationship between a pair of nodes in the network topology is represented as an edge between the pair of nodes. The influential relationship or the edge between a pair of nodes may be understood as a link or connection through which one node of the pair can share content or information with other node of the pair. The other node of the pair may get influenced by the received content or information. The influential relationship between each pair of nodes can be quantified in terms of a degree of influence of one node on the other node of the pair, depending on the shared content or information.

[0009] The degree of influence for the pairs of nodes in the network topology can be analyzed for the purpose of influence maximization. In influence maximization, a set of nodes that has a maximum spread of influence within the social network is determined. The maximum spread of influence herein may indicate that the content or information disseminated from the network users corresponding to the determined set of nodes has influence across a maximum number of network users. The procedure to determine such a set of nodes for a social network generally involves a substantially large number of computational operations. Also, the determined set of nodes is not substantially accurate. Thus, the procedure to determine the set of nodes is low on performance, and high on computational complexity, computational cost, and processing time.

[0010] The present subject matter describes methods and systems for determining a set of nodes in a social network that has a maximum spread of influence within the social network. With the methods and the systems of the present subject matter, the set of nodes that has the maximum spread of influence can be determined substantially accurately and with a substantially less number of computational operations. Thus, the methods and the systems of the present subject matter provide a high performance and involve substantially less computational complexity, computational cost, and processing time for determining the set of node.

[0011] In accordance with an example implementation of the present subject matter, the social network is modelled to determine a plurality of network users as nodes and determine an influential relationship between each pair of nodes as an edge between the respective pair of nodes. A pair of nodes may have an influential relationship, or an edge, therebetween if one node of the pair communicates with the other node of the pair through at least one mode of communication. A node may communicate with another node through one or more modes of communication. For example, in a telecommunication network, any two network users can communicate through phone calls, short message service (SMS) / multimedia message service (MMS), or application-based text/audio/video messages.

[0012] The methodology of determining a set of nodes that has a maximum spread of influence, in accordance with the present subject matter, involves iterative selection of nodes into the set of nodes based on the benefit of selection value of the nodes. The benefit of selection value of a node quantifies and indicates the benefit of selecting the node as a most influential node in the social network. For the selection of nodes, the benefit of selection value for each node is computed, and a node for which the benefit of selection value is maximum is initially selected in the set of nodes. After the initial selection of the node, the benefit of selection value of each of the neighboring nodes of the selected node is reduced. The benefit of selection value of a neighboring node of the selected node is reduced to discount for the influence of the selected node carried over to the neighboring node. As a result, a true and independent benefit of selection value of each of the neighboring nodes of the selected node is obtained and considered for the selection of nodes in the set. This helps in selecting nodes and determining the set of node with a substantial accuracy. After reducing the benefit of selection values of the neighboring nodes of the selected node, a next node, from the remaining nodes, is selected into the set of nodes for which the benefit of selection value is maximum. The procedure of reducing the benefit of selection values of neighboring nodes of an immediate previous selected node and selecting a next node into the set of node is iteratively repeated until the set of nodes has a predefined number of nodes. The predefined number may be a user-entered value.

[0013] The neighboring nodes of a selected node, for which the benefit of selection values are reduced, depend on whether one-hop neighbor nodes or two- hop neighbor nodes are considered for determining the set of nodes. When one- hop neighbor nodes are considered, the neighboring nodes include immediate successor nodes and immediate predecessor nodes of the selected node. An immediate successor node of a selected node is a node having an edge directed from the selected node. Similarly, an immediate predecessor node of a selected node is a node having an edge directed to the selected node.

[0014] Further, when two-hop neighbor nodes are considered, the neighboring nodes include immediate successor nodes and immediate predecessor nodes of the selected node, and also include further successor nodes of each of the immediate successor nodes, predecessor nodes of each of the immediate successor nodes, and further predecessor nodes of each of the immediate predecessor nodes. A further successor node of an immediate successor node is a node having an edge directed from the immediate successor node. A further predecessor node of an immediate predecessor node is a node having an edge directed to the immediate predecessor node. A predecessor node of an immediate successor node is a node having an edge directed to the immediate predecessor node.

[0015] In an example implementation, for the purpose of computing the benefit of selection value of the nodes, a degree of influence of each node on each of other nodes is computed. The degree of influence of a node on another node is computed based on the probability of influence of the node on the other node through each of the modes of communication therebetween. In an example, the probability of influence through one mode of communication may depend on the amount of content or information shared between the two nodes through that mode of communication.

[0016] In an example implementation, when one-hop neighbor nodes are considered, the benefit of selection value of a node is computed based on the degree of influence of the node on each of the immediate successor nodes of the node. In an example implementation, when two-hop neighbor nodes are considered, the benefit of selection value of a node is computed based on the degree of influence of the node on each of the immediate successor nodes of the node, and based on the degree of influence of the each immediate successor node on its each of the further successor nodes. [0017] Further, in an example implementation, when one-hop neighbor nodes are considered, in each iteration: (1) the benefit of selection value of each immediate successor node of a selected node is reduced by a factor of one minus the degree of influence of the selected node on the respective immediate successor node of the selected node; and (2) the benefit of selection value of each immediate predecessor node of the selected node is reduced by a value of the degree of influence of the respective immediate predecessor node on the selected node.

[0018] Further, in an example implementation, when two-hop neighbor nodes are considered, in each iteration: (1) the benefit of selection value of each immediate successor node of a selected node is reduced by a factor of one minus the degree of influence of the selected node on a respective immediate successor node of the selected node; (2) the benefit of selection value of each further successor node of an immediate successor node is reduced based on the degree of influence of the selected node on the immediate successor node, and the degree of influence of the immediate successor node on the respective further successor node; (3) the benefit of selection value of each predecessor node of an immediate successor node is reduced based on the degree of influence of the respective predecessor node on the immediate successor node, the degree of influence of the selected node on the immediate successor node, and the degree of influence of the immediate successor node on each of further successor nodes of the immediate successor node; (4) the benefit of selection value of each immediate predecessor node of the selected node is reduced based on the degree of influence of the respective immediate predecessor node on the selected node, and the degree of influence of the selected node on each of the immediate successor nodes of the selected nodes; and (5) the benefit of selection value of each further predecessor node of an immediate predecessor node is reduced based on the degree of influence of the respective further predecessor node on the immediate predecessor node, and the degree of influence of the immediate predecessor node on the selected node.

[0019] The following detailed description refers to the accompanying drawings. Wherever possible, the same reference numbers are used in the drawings and the following description to refer to the same or similar parts. It should be noted that the description and drawings merely illustrate the principles of the present subject matter. Therefore, various implementations that encompass the principles of the present subject matter, although not explicitly described or shown herein, can be devised from the description and are included within its scope. The word“coupled” herein may either refer to a direct connection or to an indirect connection.

[0020] Fig. 1 illustrates an influence spread maximizing system 100, according to an example implementation of the present subject matter. The influence spread maximization system 100, hereinafter referred to as the system 100, may be implemented in various ways. For example, the system 100 may be a special purpose computer, a server, a mainframe computer, and/or any other type of computing device. The system 100 enables influence maximization to determine a set of nodes that has a maximum spread of influence within a social network, in accordance with the present subject matter.

[0021] The system 100 includes processor(s) 102. The processor(s) 102 may be implemented as microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) 102 may fetch and execute computer-readable instructions stored in a memory (not shown) coupled to the processor(s) 102 of the system 100. The memory may include any non-transitory computer-readable storage medium including, for example, volatile memory (e.g., RAM), and/or non- volatile memory (e.g., EPROM, flash memory, NVRAM, memristor, etc.). The functions of the various elements shown in Fig. 1, including any functional blocks labeled as“processor(s)”, may be provided through the use of dedicated hardware as well as hardware capable of executing computer-readable instructions.

[0022] As shown in Fig. 1, the system 100 includes a network modeler 104 and an influence maximizer 106. The network modeler 104 and the influence maximizer 106 can be implemented through any suitable hardware, computer readable instructions, or a combination thereof. The network modeler 104 and the influence maximizer 106, amongst other things, may include routines, programs, objects, components, data structures, and the like, which perform particular tasks or implement particular abstract data types. The network modeler 104 and the influence maximizer 106 may be coupled to, and executed by, the processor(s) 102 to perform various functions for the purposes of determining a set of nodes that has a maximum spread of influence within a social network.

[0023] The description hereinafter describes, in detail, the procedure of determining a set of nodes that has a maximum spread of influence within a social network using the system 100. The social network may include an online social media network or a telecommunication network, in which a plurality of network users may communicate with each other to share content or information. Any two network users may communicate with each other through one or more modes of communication. In a telecommunication network, the mode of communication may include, but is not restricted to, a phone call, a SMS / MMS, and an application- based text/audio/video message. In a social media network, the mode of communication may include, but is not restricted to, an application-based text/audio/video message.

[0024] In an example implementation, for the purpose of determining the set of nodes, the network modeler 104 models the social network in the form of a network topology. The social network is modelled to determine a plurality of nodes and determine an influential relationship between each pair of nodes. Each of the plurality of nodes is determined to depict a network user in the social network. The influential relationship between a pair of nodes is depicted as an edge between the pair of nodes based on modes of communication between the pair of nodes. If a node, say Node A, shares content or information with another node, say node B, through at least one mode of communication, then node A has an influential relationship with node B. Such influential relationship is depicted by an edge directed from node A to node B. Similarly, node B shares content or information with node A through at least one mode of communication, then node B has an influential relationship with node A, and this influential relationship is depicted by an edge directed from node B to node A.

[0025] Based on the modeling of the social network, the network modeler 104 computes a degree of influence of each node on another node in the network topology. The degree of influence of each node on the other node is computed based on a probability of influence of the each node on the other node through each mode of communication therebetween. In an example, the degree of influence of any node on any other node is computed based on equation (1) below. As per equation (1), the degree of influence P_xy of a node x on a node y is computed based on:

where p_e ^xy is a probability of influence of the node x on the node y through e^th mode of communication therebetween, and R^xy is total modes of communication between the node x and the node y.

[0026] To describe the computation of the degree of influence P_xy through an example, consider a case where the node x communicates with the node y through phone calls and SMSs. For this example, R^xy = {call, SMS}. Thus, the degree of influence P_xy is computed as:

where p_call ^xy is the probability of influence of the node x on the node y through phone calls, and p_SMS ^xy is the probability of influence of the node x on the node y through SMSs.

[0027] In an example implementation, the probability of influence p_call ^xy may be proportional to a total time duration of phone calls from the node x to the node y, but saturates to a limit with increasing total time duration. Thus, the probability of influence p_call ^xy can be computed based on equation (2) below:

where P_max belongs to [0,1] and is user-defined value based on how effective the phone calls are for sharing information, k is a user-defined value based on the rate at which the probability of influence p_call ^xy saturates to P_max, and t is the total time duration of phone calls.

[0028] In an example implementation, the probability of influence p_SMS ^xy can be computed in a similar manner by replacing t, in equation (2), with number of SMSs sent by the node x to the node y. Further, in an example implementation, where the node x may also communicate with the node y through application- based text/audio/video messages, the probability of influence p_APP ^xy can be computed in a similar manner by replacing t, in equation (2), with number of application-based text/audio/video messages sent by the node x to the node y.

[0029] After computing the degree of influence of each node on each of other nodes, the influence maximizer 106 computes a benefit of selection value for the each node in the network topology. The benefit of selection value of a node is computed based on whether one-hop neighbor nodes or two-hop neighbor nodes are considered for determining the set of nodes. In an example implementation, the influence maximizer 106 may prompt a user of the system 100 to select between a one-hop neighbor nodes mode and a two-hop neighbor nodes mode of operation. The influence maximizer 106 then computes the benefit of selection value of each node depending on the mode of operation selected by the user. The details of computation of benefit of selection value for a node for the one-hop neighbor nodes mode and the two-hop neighbor nodes mode are described later in the description.

[0030] After computing the benefit of selection value for each node, the influence maximizer 106 selects a node, from the plurality of nodes, into the set of nodes, for which the benefit of selection value is maximum. This selected node may be the first node selected into the set of nodes. After selecting the node, the influence maximizer 106 recomputes the benefit of selection value of neighboring nodes of the selected node. The neighboring nodes of the selected node for which the benefit of selection values are recomputed, and the amounts by which the benefit of selection values are reduced depends on whether the system 100 is operated in the one-hop neighbor nodes mode or the two-hop neighbor nodes for determining the set of nodes. The details of neighboring nodes for a selected node and the amount by which the benefit of selection values are reduced for the one- hop neighbor nodes mode and the two-hop neighbor nodes mode are described later in the description.

[0031] After such recomputations, the influence maximizer 106 selects a next node, from the remaining nodes in the plurality of nodes, for which the benefit of selection value is maximum. In an example implementation, the influence maximizer 106 iteratively selects a next node from the remaining nodes and reduces the benefit of selection value of neighboring nodes of the next selected node, until a predefined number of nodes are selected into the set of nodes.

[0032] The description hereinafter describes the computation of benefit of selection value of a node in the network topology individually in the one-hop neighbor nodes mode of operation and the two-hop neighbor nodes mode of operation. The benefit of selection value of each node is computed in similar manner. The description also describes the recomputation of benefit of selection values of the neighboring nodes of a selected node individually in the one-hop neighbor nodes mode of operation and the two-hop neighbor nodes mode of operation. The benefit of selection values of the neighboring nodes of the node selected in each iteration are recomputed in similar manner.

[0033] For the purpose of description herein, consider an example network topology 200 shown in Fig.2. As shown, the network topology 200 includes nodes 1 to 8, referenced by 202-1 to 202-8. The edges between nodes 1 to 8 are referenced by 204-1 to 204-7. The number of edges and their direction are indicative of how many immediate successor nodes and immediate predecessor nodes each of the nodes in the network topology 200 has. For example, node 3 has two immediate successor nodes, node 4 and node 5, and has one immediate predecessor node, node 2. Similarly, node 5 has two immediate successor nodes, node 6 and node 7, and has two immediate predecessor nodes, node 3 and node 8. It may be noted that the network topology 200 with eight nodes are shown in Fig.2 as an example; however, the network topology 200 may include any number of nodes. One-hop Neighbor Nodes Mode

[0034] For the one-hop neighbor nodes mode of operation, the benefit of selection value B_u for a node u is computed based on equation (3) below:

where P_ui is the degree of influence of the node u on an immediate successor node i of the node u, and V^u _out is a set of immediate successor nodes of the node u. With reference to the example shown in Fig. 2, for computing the benefit of selection value for node Thus, the benefit of selection value for

node 3 is:

where the degree of influence P₃₄ and P₃₅ are computed based on equation (1). The benefit of selection value for each node is computed in a similar manner.

[0035] Further, consider a case where a node s is selected into the set of node. For the one-hop neighbor nodes mode of operation, the benefit of selection value of each immediate successor node of the selected node s is reduced, and the benefit of selection value for each immediate predecessor node of the selected node s is reduced. The benefit of selection value of an immediate successor node n of the selected node s is reduced by a factor of one minus the degree of influence of the selected node s on the immediate successor node n. Thus, the reduced benefit of selection value of the immediate successor node n is given by equation (4) below:

With reference to the example shown in Fig.2, if node 3 is selected into the set of nodes, then s = 3, and the benefit of selection value for node 4 is reduced to

, and the benefit of selection value for node 5 is reduced to

.

[0036] The benefit of selection value of an immediate predecessor node m of the selected node s is reduced by a value of the degree of influence of the immediate predecessor node m on the selected node s. Thus, the reduced benefit of selection value of the immediate predecessor node m is given by equation (5) below:

With reference to the example shown in Fig.2, if node 3 is selected into the set of nodes, then s = 3, and the benefit of selection value for node 2 is reduced to

Two-hop Neighbor Nodes Mode

[0037] For the two-hop neighbor nodes mode of operation, the benefit of selection value B_u for a node u is computed based on equation (6) below:

where P_ui is the degree of influence of the node u on an immediate successor node i of the node u, V^u _out is a set of immediate successor nodes of the node u, P_ij is the degree of influence of the immediate successor node i on a further successor node j of the immediate successor node i, Vⁱ _out is a set of further successor nodes of the immediate successor node i, and P_iu is the degree of influence of the immediate successor node i on the node u. With reference to the example shown in Fig.2, for computing the benefit of selection value for node

{null}, and V⁵ _out = {6,7}. Thus, the benefit of selection value for node 3 is:

The benefit of selection value for each node is computed in a similar manner.

[0038] Further, consider a case where a node s is selected into the set of node. For the two-hop neighbor nodes mode of operation, the benefit of selection values of the following neighbor nodes of the selected node s are reduced: (1) each immediate successor node of the selected node s; (2) each further successor node of the each immediate successor node of the select node s; (3) each predecessor node of the each immediate successor node of the selected node s; (4) each immediate predecessor node of the selected node s; and (5) each further predecessor node of the each immediate predecessor node of the selected node s.

[0039] The benefit of selection value of an immediate successor node n of the selected node s is reduced by a factor of one minus the degree of influence of the selected node s on the immediate successor node n, as per equation (4) mentioned earlier.

[0040] The benefit of selection value of a further successor node f of an immediate successor node n of the selected node s is reduced by a factor of wherein P_sn is the degree of influence of the selected node s on the

immediate successor node n, and P_nf is the degree of influence of the immediate successor node n on the further successor node f. Thus, the reduced benefit of selection value of the further successor node f is given by equation (7) below:

… (7)

With reference to the example shown in Fig.2, if node 3 is selected into the set of nodes, then s = 3, and the benefit of selection value for node 6 is reduced to

_{6 35 56} , and the benefit of selection value for node 7 is reduced to

[0041] The benefit of selection value of a predecessor node g of the i^{mmediate successor node n is reduced by a value of} ^{wherein Pgn is the degree of influence of the}

predecessor node g on the immediate successor node n, P_sn is the degree of influence of the selected node s on the immediate successor node n, P_ng is the degree of influence of the immediate successor node n on the predecessor node g, Pnk is the degree of influence of the immediate successor node n on a further successor node k of the immediate successor node n, Vⁿ _{out \ T} is a set of further successor nodes of the immediate successor node n that are not selected in the set of nodes, and T is the set of nodes. Thus, the reduced benefit of selection value o^{f the predecessor node g is given by equation (8) below:}

With reference to the example shown in Fig.2, if node 3 is selected into the set of nodes, then s = 3, and the benefit of selection value for node 8 is reduced to

[0042] Further, the benefit of selection value of an immediate predecessor n^{ode m of the selected node s is reduced by a value of}

, wherein P_ms is the degree of influence of the immediate predecessor node m on the selected node s, P_sm is the degree of influence of the selected node s on the immediate predecessor node m, Psk is the degree of influence of the selected node s on an immediate successor node k of the selected node s, V^s _{out \ T} is a set of immediate successor nodes of the selected node s that are not selected in the set of nodes, and T is the set of nodes. Thus, the reduced benefit of selection value of t^{he immediate predecessor node m is given by equation (9) below:}

[0043] Further, the benefit of selection value of a further predecessor node h of the immediate predecessor node m is reduced by a value of P_hm u P _ms , wherein P_hm is the degree of influence of the further predecessor node h on the immediate predecessor node m, and P_ms is the degree of influence of the immediate predecessor node m on the selected node s. Thus, the reduced benefit of selection value of the further predecessor node h is given by equation (10) below:

With reference to the example shown in Fig.2, if node 3 is selected into the set of nodes, then s = 3, and the benefit of selection value for node 1 is reduced to

[0044] Fig. 3 illustrates an example network environment 300 implementing the influence spread maximizing system 100, according to an example implementation of the present subject matter. The network environment 300 may be a public network environment or a private network environment or a combination of the two. The network environment 300 includes user devices 302-1, 302-2,… , 302-N, through which a plurality of users can access the system 100 for determining the set of nodes in social networks. The user devices 302 may include, but are not limited to, laptops, desktop computers, tablets, and the like.

[0045] Further, the user devices 302 and the system 100 may be communicatively coupled to each other through a communication network 304. The communication network 304 may be a wireless network, a wired network, or a combination thereof. The communication network 304 can also be an individual network or a collection of many such individual networks, interconnected with each other and functioning as a single large network, e.g., the Internet or an intranet. The communication network 304 can be implemented as one of the different types of networks, such as intranet, local area network (LAN), wide area network (WAN), and the internet. The communication network 304 may either be a dedicated network or a shared network, which represents an association of the different types of networks that use a variety of protocols, for example, Hypertext Transfer Protocol (HTTP) and Transmission Control Protocol/Internet Protocol (TCP/IP), to communicate with each other.

[0046] In an example implementation, the user devices 302 and the system 100 may be communicatively coupled over the communication network 304 through one or more communication links. The communication links are enabled through a desired form of communication, for example, via dial-up modem connections, cable links, and digital subscriber lines (DSL), wireless or satellite links, or any other suitable form of communication. While Fig.3 shows user devices 302 and the system 100 communicatively coupled through the communication network 304, the user devices 302 may be directly coupled to the system 100.

[0047] Further, as shown in Fig. 3, the system 100 may be communicatively coupled to a database 306 through the communication network 304. The database 306 may serve as a repository for storing data that may be fetched, processed, received, or generated by the system 100. The data includes, for example, data associated with the nodes that may be generated by system 100. The data generated by the system 100 may be transmitted to the database 306, and the data stored in the database 306 may be fetched by the system 100, over the communication network 304. Although the database 306 is shown external to the system 100, it may be understood that the database 306 can reside in the system 100. Further, while Fig. 3 shows the database 306 and the system 100 communicatively coupled through the communication network 304, the database 306 may be directly coupled to the system 100.

[0048] Fig.4 illustrates a method 400 for determining a set of nodes that has a maximum spread of influence with a social network, according to an example implementation of the present subject matter. The order in which the method 400 is described is not intended to be construed as a limitation, and any number of the described method blocks can be combined to implement the method 400. Furthermore, the method 400 can be implemented by processor(s) or computing device(s) through any suitable hardware, a non-transitory machine readable medium, or a combination thereof. Further, although the method 400 is described in context of the aforementioned influence spread maximizing system 100, other suitable computing devices or systems may be used for execution of the method 400. It may be understood that processes involved in the method 400 can be executed based on instructions stored in a non-transitory computer readable medium, as will be readily understood. The non-transitory computer readable medium may include, for example, digital memories, magnetic storage media, such as a magnetic disks and magnetic tapes, hard drives, or optically readable digital data storage media.

[0049] Referring to Fig. 4, at block 402, a benefit of selection value for each node in the social network is computed. The benefit of selection value of a node u is computed at least based on a degree of influence of the node u on each immediate successor node of the node u. The benefit of selection values of the nodes are computed by the system 100 depending of whether one-hop neighbor nodes or two-hop neighbor nodes are considered for determining the set of nodes. When one-hop neighbor nodes are considered, the benefit of selection value of each node is computed using equation (3) as described earlier. When two-hop neighbor nodes are considered, the benefit of selection value of each node is computed using equation (6) as described earlier. Further, for the purpose of computing the benefit of selection values of the nodes, the degree of influence of each node on each of other nodes is computed. The degree of influence of each node on each of the other nodes is computed by the system 100 using equation (1) as described earlier.

[0050] At block 404, a node s is selected into the set of nodes, for which the benefit of selection value is maximum. The node s is selected by the system 100 from the plurality of nodes. At block 406, the benefit of selection value of each immediate successor node of the selected node s is reduced by a factor of one minus the degree of influence of the selected node s on a respective immediate successor node n of the selected node s. At block 408, the benefit of selection value of each immediate predecessor node of the selected node s is reduced at least by a value of the degree of influence of a respective immediate predecessor node m on the selected node s.

[0051] As described earlier, the neighboring nodes of the selected node s for which the benefit of selection values are reduced and the amount of by which the benefit of selection values are reduced depends on whether one-hop neighbor nodes or two-hop neighbor nodes are considered for determining the set of nodes. When one-hop neighbor nodes are considered, the benefit of selection values of the immediate successor nodes and the immediate predecessor nodes of the selected node s are reduced by the system 100 using equations (4) and (5), respectively. When two-hop neighbor nodes are considered, the benefit of selection values of: (1) the immediate successor nodes of the selected node s; (2) the further successor nodes of each immediate successor node of the selected node s; (3) the predecessor nodes of each immediate successor node of the selected node s; (4) the immediate predecessor nodes of the selected node s; and (5) the further predecessor nodes of each immediate predecessor node of the selected node s, are reduced based on equations (4), (7), (8), (9), and (10), respectively.

[0052] After reducing the benefit of selection value, at block 410, a next node is selected, from remaining nodes, into the set of nodes, for which the benefit of selection value is maximum. The next node is selected by the system 100. Further, when one-hop neighbor nodes are considered, the benefit of selection values of each immediate successor node of the next selected node and each immediate predecessor node of the next selected node are iteratively reduced, and a further node, from remaining nodes, for which the benefit of selection value is maximum is iteratively selected into the set of nodes, until a predefined number of nodes are selected into the set of nodes. Also, when two-hop neighbor nodes are considered, the benefit of selection values of each immediate successor node of the next selected node, each immediate predecessor node of the next selected node, each predecessor node of the each immediate successor node, each further successor node of the each immediate successor node and each further predecessor node of the each immediate predecessor node are iteratively reduced, and a further node, from remaining nodes, for which the benefit of selection value is maximum is iteratively selected into the set of nodes, until a predefined number of nodes are selected into the set of nodes.

[0053] Fig.5 illustrates an example network environment 500 for determining a set of nodes that has a maximum spread of influence with a social network, according to an example implementation of the present subject matter. The network environment 500 may be a public networking environment or a private networking environment. In an example implementation, the network environment 500 includes a computer 502 communicatively coupled to a non-transitory computer readable medium 504 through a communication link 506. In an example, the computer 502 may be the influence spread maximizing system 100 having one or more processing resources for fetching and executing computer-readable instructions from the non-transitory computer readable medium 504.

[0054] The non-transitory computer readable medium 504 can be, for example, an internal memory device or an external memory device. In an example implementation, the communication link 506 may be a direct communication link, such as any memory read/write interface. In another example implementation, the communication link 506 may be an indirect communication link, such as a network interface. In such a case, the computer 502 can access the non-transitory computer readable medium 504 through a network 508. The network 508 may be a single network or a combination of multiple networks and may use a variety of different communication protocols.

[0055] The computer 502 and the non-transitory computer readable medium 504 may also be communicatively coupled to data sources 510 over the network 508. The data sources 510 can include, for example, user devices through which users can access the computer 502 or the influence spread maximizing system 100. The data sources 510 may also include a database that serves as a repository for storing data that may be fetched, processed, received, or generated by the computer 502.

[0056] In an example implementation, the non-transitory computer readable medium 504 includes a set of computer readable instructions for determining a set of nodes that has a maximum spread of influence with a social network. The set of computer readable instructions can be accessed by the computer 502 through the communication link 506 and subsequently executed to perform acts for determining the set of nodes.

[0057] Referring to Fig. 5, in an example, the non-transitory computer readable medium 504 includes instructions 512 that cause the computer 502 to compute a benefit of selection value for each node in the social network, where the benefit of selection value of a node u is computed at least based on a degree of influence of the node u on each immediate successor node of the node u. The non- transitory computer readable medium 504 includes instructions 514 that cause the computer 502 to select a node s into the set of nodes, for which the benefit of selection value is maximum. The non-transitory computer readable medium 504 also includes instructions 516 that cause the computer 502 to reduce the benefit of selection value of each immediate successor node of the selected node s by a factor of one minus the degree of influence of the selected node s on a respective immediate successor node n of the selected node s, and includes instructions 518 that cause the computer 502 to reduce the benefit of selection value of each immediate predecessor node of the selected node s at least by a value of the degree of influence of a respective immediate predecessor node m on the selected node s. The non-transitory computer readable medium 504 further includes instructions 520 that cause the computer 502 to iteratively select, into the set of nodes, a next node from remaining nodes for which the benefit of selection value is maximum, and reduce the benefit of selection value of each immediate successor node of the next selected node and each immediate predecessor node of the next selected node, until a predefined number of nodes are selected into the set of nodes.

[0058] In an example implementation, the non-transitory computer readable medium 504 includes instructions that cause the computer 502 to compute the benefit of selection value of each node using equation (3), and reduce the benefit of selection values using equations (4) and (5), as described earlier, when one-hop neighbor nodes are considered. In an example implementation, the non-transitory computer readable medium 504 includes instructions that cause the computer 502 to compute the benefit of selection value of each node using equation (6), and reduce the benefit of selection values using equations (7) to (10), as described earlier, when two-hop neighbor nodes are considered.

[0059] Although implementations for determining a set of nodes that has a maximum spread of influence within a social network have been described in language specific to structural features and/or methods, it is to be understood that the present subject matter is not necessarily limited to the specific features or methods described. Rather, the specific features and methods are disclosed and explained as example implementations for determining a set of nodes that has a maximum spread of influence within a social network.

Claims

We claim: 1. A method for determining a set of nodes that has a maximum spread of influence within a social network, the method comprising:

computing, by a computing device, a benefit of selection value for each node in the social network, wherein the benefit of selection value of a node u is computed at least based on a degree of influence of the node u on each immediate successor node of the node u;

selecting, by the computing device, a node s into the set of nodes, for which the benefit of selection value is maximum;

reducing, by the computing device, the benefit of selection value of each immediate successor node of the selected node s by a factor of one minus the degree of influence of the selected node s on a respective immediate successor node n of the selected node s;

reducing, by the computing device, the benefit of selection value of each immediate predecessor node of the selected node s at least by a value of the degree of influence of a respective immediate predecessor node m on the selected node s; and

selecting, into the set of nodes, a next node from remaining nodes for which the benefit of selection value is maximum.

2. The method as claimed in claim 1, comprising:

computing, by the computing device, a degree of influence of each node on each of other nodes in the social network, wherein the degree of influence of a node x on a node y is computed based on:

wherein p_e ^xy is a probability of influence of the node x on the node y through e^th mode of communication therebetween, and R^xy is total modes of communication between the node x and the node y.

3. The method as claimed in claim 1, wherein, when one-hop neighbor nodes are considered for determining the set of nodes, the benefit of selection value for the node u is computed based on:

wherein P_ui is the degree of influence of the node u on an immediate successor node i of the node u, and V^u _out is a set of immediate successor nodes of the node u.

4. The method as claimed in claim 3, comprising:

iteratively reducing the benefit of selection values of each immediate successor node of the next selected node and each immediate predecessor node of the next selected node, and selecting a further node from remaining nodes into the set of nodes, for which the benefit of selection value is maximum, until a predefined number of nodes are selected into the set of nodes.

5. The method as claimed in claim 1, wherein, when two-hop neighbor nodes are considered for determining the set of nodes, the benefit of selection value for the ^{node u is com uted based on:}

wherein P_ui is the degree of influence of the node u on an immediate successor node i of the node u, V^u _out is a set of immediate successor nodes of the node u, P_ij is the degree of influence of the immediate successor node i on a further successor node j of the immediate successor node i, Vⁱ _out is a set of further successor nodes of the immediate successor node i, and P_iu is the degree of influence of the immediate successor node i on the node u.

6. The method as claimed in claim 5, comprising:

reducing, by the computing device, the benefit of selection value of each further successor node of the respective immediate successor node n, wherein the benefit of selection value of a further successor node f of the respective i^{mmediate successor node n is reduced by a factor of , wherein P} _sn

is the degree of influence of the selected node s on the respective immediate successor node n, and P_nf is the degree of influence of the respective immediate successor node n on the further successor node f; and

reducing, by the computing device, the benefit of selection value of each predecessor node of the respective immediate successor node n, wherein the benefit of selection value of a predecessor node g of the respective immediate s^{uccessor node n is reduced by a value of}

wherein P_gn is the degree of influence of the predecessor node g on the respective immediate successor node n, P_sn is the degree of influence of the selected node s on the respective immediate successor node n, Png is the degree of influence of the respective immediate successor node n on the predecessor node g, P_nk is the degree of influence of the respective immediate successor node n on a further successor node k of the respective immediate successor node n, Vⁿ _{out \ T} is a set of further successor nodes of the respective immediate successor node n that are not selected in the set of nodes, and T is the set of nodes.

7. The method as claimed in claim 5, comprising:

reducing, by the computing device, the benefit of selection value of the r^{espective immediate predecessor node m of the selected node s by a value of}

,^{wherein Pms is the degree of influence of the}

respective immediate predecessor node m on the selected node s, P_sm is the degree of influence of the selected node s on the respective immediate predecessor node m, P_sk is the degree of influence of the selected node s on an immediate successor node k of the selected node s, V^s _{out \ T} is a set of immediate successor nodes of the selected node s that are not selected in the set of nodes, and T is the set of nodes; and

reducing, by the computing device, the benefit of selection value of each further predecessor node of the respective immediate predecessor node m, wherein the benefit of selection value of a further predecessor node h of the respective immediate predecessor node m is reduced by a value of

wherein P_hm is the degree of influence of the further predecessor node h on the respective immediate predecessor node m, and P_ms is the degree of influence of the respective immediate predecessor node m on the selected node s.

8. The method as claimed in claim 5, comprising:

iteratively reducing the benefit of selection values of each immediate successor node of the next selected node, each immediate predecessor node of the next selected node, each predecessor node of the each immediate successor node, each further successor node of the each immediate successor node, and each further predecessor node of the each immediate predecessor node, and selecting a further node from remaining nodes into the set of nodes, for which the benefit of selection value is maximum, until a predefined number of nodes are selected into the set of nodes.

9. An influence spread maximizing system for determining a set T of nodes that has a maximum spread of influence within a social network, the influence spread maximizing system comprising:

a processor;

a network modeler coupled to the processor to:

determine a plurality of nodes in the social network and an influential relationship between each pair of nodes based on modes of communication between a respective pair of nodes; and

compute a degree of influence of each node on another node based on a probability of influence of the each node on the other node through each mode of communication therebetween; and

an influence maximizer coupled to the processor to:

compute a benefit of selection value for the each node, wherein the benefit of selection value of a node u is computed at least based on the degree of influence of the node u on each immediate successor node of the node u;

select a node s, from the plurality of nodes, into the set T of nodes, for which the benefit of selection value is maximum; recompute the benefit of selection value of each immediate successor node of the selected node s based on a factor of one minus the degree of influence of the selected node s on a respective immediate successor node n of the selected node s;

recompute the benefit of selection value of each immediate predecessor node of the selected node s at least based on a value of the degree of influence of a respective immediate predecessor node m on the selected node s; and

iteratively select, into the set of nodes, a next node from remaining nodes in the plurality of nodes for which the benefit of selection value is maximum, and reduce the benefit of selection value of each immediate successor node of the next selected node and each immediate predecessor node of the next selected node, until a predefined number of nodes are selected into the set of nodes.

10. The influence spread maximizing system as claimed in claim 9, wherein, when one-hop neighbor nodes are considered for determining the set of nodes, the benefit of selection value for the node u is computed based on:

11. The influence spread maximizing system as claimed in claim 9, wherein, when two-hop neighbor nodes are considered for determining the set of nodes, the ^{benefit of selection value for the node u is computed based on:}

12. The influence spread maximizing system as claimed in claim 11, wherein the influence maximizer is to:

recompute the benefit of selection value of each further successor node of the respective immediate successor node n, wherein the benefit of selection value of a further successor node f of the respective immediate successor node n is reduced by a factor of , wherein P_sn is the degree of influence

of the selected node s on the respective immediate successor node n, and Pnf is the degree of influence of the respective immediate successor node n on the further successor node f;

recompute the benefit of selection value of each predecessor node of the respective immediate successor node n, wherein the benefit of selection value of a predecessor node g of the respective immediate successor node n is r^{educed by a value of , wherein Pgn is the degree}

of influence of the predecessor node g on the respective immediate successor node n, P_sn is the degree of influence of the selected node s on the respective immediate successor node n, P_ng is the degree of influence of the respective immediate successor node n on the predecessor node g, P_nk is the degree of influence of the respective immediate successor node n on a further successor node k of the respective immediate successor node n, Vⁿ _{out \ T} is a set of further successor nodes of the respective immediate successor node n that are not selected in the set of nodes, and T is the set of nodes;

recompute the benefit of selection value of the respective immediate p^{redecessor node m of the selected node s based on a value of}

,^{wherein Pms is the degree of influence of the}

recompute the benefit of selection value of each further predecessor node of the respective immediate predecessor node m, wherein the benefit of selection value of a further predecessor node h of the respective immediate predecessor node m is reduced by a value of P_hm u P _ms , wherein P_hm is the degree of influence of the further predecessor node h on the respective immediate predecessor node m, and P_ms is the degree of influence of the respective immediate predecessor node m on the selected node s.

13. A non-transitory computer-readable medium comprising computer-readable instructions, which, when executed by a computer, cause the computer to:

compute a benefit of selection value for each node in the social network, wherein the benefit of selection value of a node u is computed at least based on a degree of influence of the node u on each immediate successor node of the node u;

select a node s into the set of nodes, for which the benefit of selection value is maximum;

reduce the benefit of selection value of each immediate successor node of the selected node s by a factor of one minus the degree of influence of the selected node s on a respective immediate successor node n of the selected node s;

reduce the benefit of selection value of each immediate predecessor node of the selected node s at least by a value of the degree of influence of a respective immediate predecessor node m on the selected node s; and

iteratively select, into the set of nodes, a next node from remaining nodes for which the benefit of selection value is maximum, and reduce the benefit of selection value of each immediate successor node of the next selected node and each immediate predecessor node of the next selected node, until a predefined number of nodes are selected into the set of nodes.

14. The non-transitory computer-readable medium as claimed in claim 13, wherein ^{the benefit of selection value for the node u is computed based on:}

15. The non-transitory computer-readable medium as claimed in claim 13, wherein the instructions which, when executed by the computer, cause the computer to: reduce the benefit of selection value of each further successor node of the respective immediate successor node n, wherein the benefit of selection value of a further successor node f of the respective immediate successor node n is reduced by a factor of 1^ P_sn u P _nf , wherein P_sn is the degree of influence of the selected node s on the respective immediate successor node n, and P_nf is the degree of influence of the respective immediate successor node n on the further successor node f;

reduce the benefit of selection value of each predecessor node of the respective immediate successor node n, wherein the benefit of selection value of a predecessor node g of the respective immediate successor node n is r^{educed by a value of wherein Pgn is the degree}

of influence of the predecessor node g on the respective immediate successor node n, P_sn is the degree of influence of the selected node s on the respective immediate successor node n, P_ng is the degree of influence of the respective immediate successor node n on the predecessor node g, P_nk is the degree of influence of the respective immediate successor node n on a further successor node k of the respective immediate successor node n, Vⁿ _{out \ T} is a set of further successor nodes of the respective immediate successor node n that are not selected in the set of nodes, and T is the set of nodes; reduce the benefit of selection value of the respective immediate ^{predecessor node m of the selected node s by a value of}

,^{wherein Pms is the degree of influence of the}

reduce the benefit of selection value of each further predecessor node of the respective immediate predecessor node m, wherein the benefit of selection value of a further predecessor node h of the respective immediate predecessor ^{node m is reduced by a value of wherein P} _hm ^{is the degree of}

influence of the further predecessor node h on the respective immediate predecessor node m, and P_ms is the degree of influence of the respective immediate predecessor node m on the selected node s.