Patent Publication Number: US-2016232161-A1

Title: Method to maximize message spreading in social networks and find the most influential people in social media

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to and is a non-provisional of U.S. Patent Application Ser. No. 62/101,756 (filed Jan. 9, 2015) the entirety of which is incorporated herein by reference. 
    
    
     STATEMENT OF FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with Government support under contract number NSF-PHY #1305476 awarded by the National Science Foundation; Contract Number W911NF-09-2-0053 awarded by the Army Research Laboratory and Contract Number NIH-NIGMS 1R21GM107641-01 awarded by the National Institute of Health. The government has certain rights in the invention. 
    
    
     BACKGROUND OF THE INVENTION 
     The subject matter disclosed herein relates to social networking and, more particularly, to the viral distribution of data within a social network. 
     Information spreading is an ubiquitous process in society which describes a variety of phenomena ranging from the adoption of innovations, the success of commercial promotions, the rise of political movements, and the spread of news, opinions and brand new products in society. In these phenomena, starting from a few “seeds”, the information spreads from person to person contagiously and may eventually reach the majority of population in a “viral” way. As such, how people contact each other in a social network is of great significance in information spreading processes. However, not all people are equally important in a social network. Some influential individuals stand out due to their prominent ability to spread opinion to the largest populations. The ability to initiate a “viral” spreading process starting at these most influential individuals is attributed to the spreader&#39;s unique location in the underlying social network. Targeting these most influential people in information dissemination is crucial for designing strategies for accelerating the speed of propagation in product promotion during advertisement and marketing campaigns in online social networks. Therefore, identification of the most influential spreaders in social networks is of great practical importance. 
     A number of different measures aimed at identifying influential spreaders were suggested over the years. The most prominent ones include the degree of an individual (number of links, connections or friends in a social network), PAGERANK®, and betweenness centrality. Degree is the most direct and widely-used topological measure of influence. In a social network with a broad degree distribution, the most connected people or hubs are usually believed to be responsible for the largest spreading processes. PAGERANK® is a network-based diffusion method which describes a random walk process on hyperlinked networks. Although, it was originally proposed to rank content in the World Wide Web and stimulated the revolution in the web search industry contributing to the emergence of the search giant GOOGLE®, PAGERANK® is applied in many circumstances to rank an extensive array of data. Due to their straightforward implementation, researchers use the degree and PAGERANK® to identify influential individuals in social networks in many practical situations. Betweenness centrality is defined as a measure of how many shortest paths cross through a node and is also used to identify the influential individuals by their high betweeness centrality. 
     A major drawback of the above referenced methods is the inability to capture the collective behavior of identified influential nodes and the detection of optimal set of multiple influencers providing full network coverage according to a given information spreading protocol. Thus, the widely-used degree centrality and PAGERANK® methods fail in ranking users&#39; influence. 
     The discussion above is merely provided for general background information and is not intended to be used as an aid in determining the scope of the claimed subject matter. 
     BRIEF DESCRIPTION OF THE INVENTION 
     A method is provided to maximize the spreading of information in social networks. The method identifies the most influential nodes by introducing a ranking method based on collective behavior of nodes in a social network. The method is then used to identify the minimal set of such nodes that are able to spread information in the network. An advantage that may be realized in the practice of some disclosed embodiments of the method is that influential spreaders of information in a large social network can be more easily identified for subsequent distribution of data. 
     In a first embodiment, a method to distribute data in a social network is provided. The method comprises steps of determining a topological structure of a social network, wherein the social network comprises a plurality of individuals including influential spreaders of information; calculating a collective influence (CI) value for each individual (i) on other individuals (j) in the social network within a radius link ( 4  identifying the individual with the highest CI value as a top influential spreader and thereafter (1) adding the top influential spreader to a rank ordered list of influential spreaders and (2) removing the top influential spreader from the social network and (3) repeating, for each individual (j) that was directly linked to the top influential spreader, the steps of calculating, identifying, adding and removing until all individuals in the social network have a CI value of zero; and sending data to at least one individual on the rank ordered list of influential spreaders for subsequent dissemination over the social network. 
     In a second embodiment, a method to distribute data in a social network is provided. The method comprising steps of determining a topological structure of a social network, wherein the social network comprises a plurality of individuals including influential spreaders of information; calculating a collective influence (CI) value for each individual (i) on other individuals (j) in the social network according to: 
       CI l ( i )=( k   i −1)Σ jε∂Ball(i,l) ( k   j −1)
 
     wherein k i  is a degree of individual (i), k j  is a degree of individual (j), ∂Ball(i, l) is a ball of radius l around individual (i), wherein l is a non-zero integer corresponding to a number of links to connect individuals; identifying the individual with the highest CI value as a top influential spreader and thereafter (1) adding the top influential spreader to a rank ordered list of influential spreaders and (2) removing the top influential spreader from the social network and (3) repeating, for each individual (j) that was directly linked to the top influential spreader, the steps of calculating, identifying, adding and removing until all individuals in the social network have a CI value of zero; and sending data to at least one individual on the rank ordered list of influential spreaders for subsequent dissemination over the social network. 
     This brief description of the invention is intended only to provide a brief overview of subject matter disclosed herein according to one or more illustrative embodiments, and does not serve as a guide to interpreting the claims or to define or limit the scope of the invention, which is defined only by the appended claims. This brief description is provided to introduce an illustrative selection of concepts in a simplified form that are further described below in the detailed description. This brief description is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used as an aid in determining the scope of the claimed subject matter. The claimed subject matter is not limited to implementations that solve any or all disadvantages noted in the background. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       So that the manner in which the features of the invention can be understood, a detailed description of the invention may be had by reference to certain embodiments, some of which are illustrated in the accompanying drawings. It is to be noted, however, that the drawings illustrate only certain embodiments of this invention and are therefore not to be considered limiting of its scope, for the scope of the invention encompasses other equally effective embodiments. The drawings are not necessarily to scale, emphasis generally being placed upon illustrating the features of certain embodiments of the invention. In the drawings, like numerals are used to indicate like parts throughout the various views. Thus, for further understanding of the invention, reference can be made to the following detailed description, read in connection with the drawings in which: 
         FIG. 1A  depicts the largest eigenvalue λ of   exemplified on a simple network; 
         FIG. 1B  depicts an example of non-backtracking (NB) walks. A NB walk is a random walk that is not allowed to return back along the edge that it just traversed; 
         FIG. 1C  is a representation of the global minimum over n of the largest eigenvalue λ of   versus q; 
         FIG. 1D  depicts a ball(i, l) of radius l around node i is the set of nodes at distance l from i, and ∂Ball is the set of nodes on the boundary; 
         FIG. 1E  is an example of a weak node: a node with a small number of connections surrounded by hierarchical coronas of hubs at different l levels; 
         FIG. 2A  depicts a Giant component G(q) of TWITTER® users (N=469, 013) computed using CI, HDA, PAGERANK®, HD and k-core strategies; 
         FIG. 2B  depicts G(q) for a social network of N=14, 346, 653 mobile phone users in Mexico representing an example of big data to test the scalability and performance of the method in real networks; 
         FIG. 3A  to  FIG. 3I  depict an example of the execution of the disclosed method; 
         FIG. 4A  a, G(q) in an Erdos-Renyi synthetic network (N=200, 000) showing the true optimal solution found with EO (‘x’ symbol), and also using CI, HDA, PR, HD, CC, EC and k-core methods; 
         FIG. 4B  shows G(q) for a Scale-Free synthetic network with N=200, 000 nodes. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     A method is provided to systematically identify the most influential individuals in a large social network. The successful identification of these influential individuals, in turn, can be used for a number of practical applications. For example, the role of these influential nodes to act as super spreaders in large online social networks such as FACEBOOK® and TWITTER® may be used. Identification of super spreaders helps to develop targeted marketing strategies in an optimal way (e.g. place advertisements on the walls and blogs of influential individuals in online social networks) which in turn supports the efficient spreading of information through online social media. 
     Conventional techniques for identifying influential individuals suffer from a major drawback in that they try to identify the structural importance of a single node (a single person in the network) completely or partially independent of the importance of other nodes. As a result the eventual set of influential nodes found for any network is a sub-optimal solution. The disclosed method takes into account the complex interconnectivity of a network and identifies an optimal set of nodes that are capable of spreading information in the entire network in the fastest possible way, thus facilitating viral spreading marketing campaigns. 
     The disclosed method is equally applicable in creating a containment plan against a possible viral outbreak and identifying weak infrastructural links in networks such as computer networks, electrical power grids and roads. Other applications include protein-protein interaction networks in cellular biology, air transport networks in transportation systems, cell phone communication towers in communication engineering, social collaboration networks of movie actors or researchers in sociology, development strategies of cities in urban geography. In brief, wherever real-world interconnected systems can be modeled as networks with nodes and edges, the disclosed method can be used to identify influential nodes, which in turn can be utilized in several different ways to solve real-world problems. 
     In a broader sense, influence is deeply related to the concept of cohesion of a network: the most influential nodes are the ones forming the minimal set that guarantees a global connection of the network. This minimal set is referred to as the ‘optimal influencers’ of the network. At a general level, the optimal influence problem can be stated as follows: find the minimal set of nodes which, if removed, would break down the network into many disconnected pieces. The natural measure of influence is, therefore, the size of the largest connected component as the influencers are removed from the network. 
     An optimization theory of influence in complex social networks is provided herein. A network composed of N nodes tied with M links with an arbitrary degree distribution is considered. A certain fraction q of the total number of nodes may be removed. It is well known from percolation theory that, if these nodes are removed randomly, the network undergoes a structural collapse at a certain critical fraction where the probability of existence of the giant connected component vanishes, G=0. The optimal influence problem corresponds to finding the minimum fraction q c  of influencers to fragment the network: q c =min{qε[0,1]: G(q)=0}. 
     Let the vector n=(n 1 , . . . , n N ) represent which node is removed (n i =0, influencer) or left (n i =1, the rest) in the network (q=1−1/NΣ i n i ), and consider a link from i→j. The order parameter of the percolation transition is the probability that i belongs to the giant component in a modified network where j is absent, v i→j . 
     Clearly, in the absence of a giant component the solution {v i→j =0} holds true for all i→j. The stability of the solution {v i→j =0} is controlled by the largest eigenvalue λ (n; q) of the linear operator   defined on the 2M×2M directed edges as (see  FIG. 1A ) 
           k→l,i→j   =n   i     k→l,i→j   (1)
 
     where    k→l,i→j  is the non-backtracking matrix.  FIG. 1A  depicts the largest eigenvalue λ of   exemplified on a simple network. The optimal strategy for spreading minimizes λ by removing the minimum number of nodes (optimal influencers). In the left panel of  FIG. 1A , the entry    2→3,3→5 =n 3     2→3,3→5 =n 3  encodes the occupancy (n 3 =1) or vacancy (n 3 =0) of node  3 . In this particular case, the largest eigenvalue is λ=1. In the center panel of  FIG. 1A , non-optimal removal of a leaf, n 4 =0, which does not decrease λ. In the right panel of  FIG. 1A , optimal removal of a loop, n 3 =0, which decreases λ to zero. The matrix    k→l,i→j  has non-zero entries only when (k→l, i→q) form a pair of consecutive non-backtracking directed edges, i.e. (k→l, l→j) with j≠k. In this case    k→l,l→j =1. Powers of the matrix   count the number of non-backtracking walks of a given length in the network (see  FIG. 1B ), much in the same way as powers of the adjacency matrix count the usual number of paths.  FIG. 1B  depicts an example of non-backtracking (NB) walks. A NB walk is a random walk that is not allowed to return back along the edge that it just traversed. A NB open walk (l=3), a NB closed walk with a tail (l=4), and a NB closed walk with no tails (l=5) are shown. Operator   is also important in graph theory due to its high performance in the problem of community detection. Its formidable topological power in the influence optimization problem is shown next. 
     Stability of the solution {v i→j =0} requires λ (n; q)≦1. The optimal influence problem for a given q(≧q c ) can be rephrased as finding the optimal configuration n that minimizes the largest eigenvalue λ (n; q) over all possible configurations n (see  FIG. 1C ).  FIG. 1C  is a representation of the global minimum over n of the largest eigenvalue λ of   versus q. When q≧q c , the minimum is at λ=0. When q&lt;q c , the minimum of the largest eigenvalue is always λ&gt;1. At the optimal percolation transition, the minimum is at n* with λ(n*, q c )=1. The optimal set n* of Ng c  influencers is obtained when the minimum of the largest eigenvalue reaches the critical threshold: 
       λ( n*;q   c )=1  (2)
 
     In the optimized case, the method selects the set n i =0 optimally to find the best configuration n* with the lowest q c  according to Eq. (2). The eigenvalue λ (n) (from now q is omitted λ (n; q)≡λ(n), which is always kept fixed) determines the growth rate of an arbitrary vector w 0  with 2M entries after l iterations of the matrix  : |w l (n)|=|   l w 0 |˜e l log λ(n) . More precisely: 
     
       
         
           
             
               
                 
                   
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     Equation (3) is the starting point of an (infinite) perturbation series which provides the exact solution to the many-body influence problem and therefore contains all physical effects, including the collective influence. In practice, the cost energy function of influence |w l (n)| is minimized for a finite l. The solution rapidly converges to the exact value as l→∞, the faster the larger the spectral gap. For l≧1: 
       | w   l ( n )| 2 =Σ i=1   N ( k   i −1)Σ jε∂Ball(i,l) (Π kε       l     (i,j)   n   k )( k   j −1)  (4)
 
     where Ball(i, l) is the set of nodes inside a ball of radius l around node i, ∂Ball(i, l) is the frontier of the ball and    l (i, j) is the shortest path of length l connecting i and j (see  FIG. 1D ), and k i  is the degree of node i. 
     The case of zero radius l=0 leads to &lt;w 0 | |w 0 &gt;=Σ i   N k i  (k i −1)n i . Here, there is no interaction between the nodes and the minimization of λ (n) over n naturally leads to the high degree (HD) ranking as the zero-order naive optimization in the disclosed method. 
     The next level in the collective influence optimization in Eq. (4) is l=1. The term |w 1 (n) 2 |=Σ i,j=1   N A ij (k i −1)(k j −1)n i n j  is found, where A ij  is the adjacency matrix. This term is interpreted as the energy of an antiferromagnetic Ising spin model with random bonds in a random external field at fixed magnetization, which is an example of an NP-complete spin glass problem. 
     For l≧2, the problem can be mapped to a statistical mechanical system with many-body interactions which can be recast in terms of a diagrammatic expansion. For example, w 2 (n) 2  leads to 4-body interactions, and, in general, the energy cost w l (n) 2  contains 2l-body interactions. When l≧2 an extremal optimization (EO) method can be used to find the optimal configuration. This method estimates the true optimal value of the threshold by finite-size scaling following extrapolation to l→∞. However, EO is not scalable to find the optimal configuration in large networks in present day social media. For example, EO becomes untenable for networks larger than about one hundred users. Therefore, an adaptive method was developed, which performs excellently in practice, preserves the features of the EO, and is highly scalable to present-day big data. The disclosed method is applicable to networks with over 100 people, and in some embodiments, over one million people. In still other embodiments, 100 million or more people are present in the network. 
     Thus a method is provided to identify super spreaders called Collective Influence (CI). In one embodiment, the CI method is implemented in C++. It takes as input a social network and outputs a ranking of influential spreaders. The method is described below: 
     First, a ball of radius l around every node is defined (see  FIG. 1D ). Then, the nodes belonging the frontier ∂Ball(i,l) are considered and node i is assigned the collective influence (CI) strength at level l following Eq. (4): 
       CI l ( i )=( k   i =1)Σ jε∂Ball(i,l) ( k   j −1)  (5)
 
     Once the CI is calculated for every node, the nodes are ranked with respect to CI and the node having the highest value of CI, say node i*, is considered to be the most influential node in the network. Then, node i* is removed from the network and n i*  (set n i =0), and the degree of each neighbor of i* is decreased by one. Using the obtained reduced network, the procedure is repeated to find the new top CI node. This top CI node is assigned as the second most important influencer and then removed from the network along with all its links. The method then proceeds by identifying the next top CI node and then removing it. The method is terminated when all top influencers are identified. This corresponds to the minimum number of influencers that reduces the giant connected component of the network to zero, G=0. Thus, the CI method is terminated when the last influencer is identified and G=0. The CI method is illustrated in  FIGS. 3A to 3I , where it is shown how the CI method finds the most influential people to target in a viral marketing campaign in a small portion of the TWITTER® social network for illustrative purposes. 
     Increasing the radius l of the ball improves the approximation of the optimal exact solution as l→∞ (for finite networks, l does not exceed the network diameter). 
     The collective influence CI l  for l→1 has a rich topological content, and consequently gives more informations about the role played by nodes in the network than the non-interacting high-degree hub-removal strategy at l=0, CI 0 . The augmented information comes from the sum in the right hand side of Eq. (5), which is absent in the naive high-degree rank. This sum contains the contribution of the nodes living on the surface of the ball surrounding the central vertex i, each node weighted by the factor k j −1. This means that a node placed at the centre of a corona irradiating many links—the structure hierarchically emerging at different levels as seen in  FIG. 1E —can have a very large collective influence, even if it has a moderate or low degree. Such ‘weak nodes’ can outrank nodes with larger degree that occupy mediocre peripheral locations in the network. 
     As an example of an information spreading network, the web of TWITTER® users is considered. TWITTER® is the online social networking and microblogging service that has gained world-wide popularity. A dataset of approximately 16 million tweets sampled between Jan. 23 and Feb. 8, 2011 and is used. From these tweets the mention network is extracted. Mentions are tweets containing @username and usually include personal conversations or references. In fact, the mention links have stronger strength of ties than follower links. Therefore, the mention network can be viewed as a stronger version of interactions between TWITTER® users. In the mention network, if user i mentions user j in his/her tweets, there exists a link from i to j. In order to better represent the social contacts, the retweet relations from the tweets are also added to the network. A retweet (RT @username) corresponds to content forward with the specified user as the nominal source. If user i retweets a tweet of user j, then a contact is established between j and i. In this way, the social network of Twitter is constructed. The resulting network has N=469, 013 nodes and M=913, 457 links. As explained above, the collective influence of a group of nodes is measured as the drop in the size of the giant component G which would happen if the nodes in question were removed from the network. The results in  FIG. 2A  show the giant connected component G of the Twitter network as a function of the fraction q of nodes removed following different strategies: the CI method, High-Degree (HD), High-Degree Adaptive (HDA), PAGERANK® and k-core. This plot shows the better performance of CI in comparison with HDA, PAGERANK®, HD and k-core, since CI is able to fragment the giant component G=0 with the smallest fraction q of influencers. Thus, CI identifies the optimal influencers as opposed to the other strategies which are non-optimal. The plot also reveals that many individuals with a large number of followers (high degree) have a small influence on the network and are poor spreaders of information. This indicates that people with a large number of connections are not necessarily the most influential individuals in the network. 
     As shown in  FIG. 3A , to illustrate how the CI method finds the most influential people to target in TWITTER®, a small portion of the full network is extracted, composed of 20 people and 36 links. The parameter l in the CI method is set to l=2. The topological structure of the network is the individuals and the social network links relating those individuals. The detailed step by step explanation of the method in this specific case is provided in  FIGS. 3A to 3I . 
     In  FIG. 3B , the method finds the individual with the highest CI value. In the embodiment of  FIG. 3B , individual 19 with a CI value of 135 is found. This value is calculated according to Eq. (5) as follows. First the number of connections minus one of individual number 19 is considered: k 19 −1=6−1=5. Then all the people two links away from individual 19 are considered (i.e. l=2), which are the individuals numbered 7, 14, 11, 16, 12, 3, 13, 1, 18. The number of connections minus one of those individuals are considered: k 7 −1=4; k 14 −1=3; k 11 −1=2; k 16 −1=2; k 12 −1=5; k 3 −1=4; k 13 −1=2; k 1 −1=3; k 18 −1=2; and then summed up: (k 7 −1)+(k 14 −1)+(k 11 −1)+(k 16 −1)+(k 12 −1)+(k 3 −1)+(k 13 −1)+(k 1 −1)+(k 18 −1)=4+3+2+2+5+4+2+3+2=27. Then this sum is multiplied by k 19 −1=5, to get the final result: (k 19 −1)×27=5×27=135. Individual 19 is assigned as the first target in the marketing campaign and then removed from the network along with all its links. Then, the number of connections of all the people linked with individual 19 are decreased by one and the CI values of those individuals are re-calculated. These are the individuals numbered 20,17,10,9,4,2. The number of connections of those individuals before the removal of individual 19 is: k 20 =3, k 17 =4, k 10 =2, k 9 =1, k 4 =7, k 2 =4. After the removal of individual 19 the number of connections of people numbered 20,17,10,9,4,2 are: k 20 =2, k 17 =3, k 10 =1, k 9 =0, k 4 =6, k 2 =3. 
     In  FIG. 3C , the method finds the next individual with the highest CI value. In the embodiment of  FIG. 3C , individual 7, whose CI value is 76 is found. As before, individual 7 is removed from the network along with all its links, and the number of connections of all people linked with individual 7 are decreased by one. This process is repeated until the CI value for all individuals in the network is zero. For example, in  FIG. 3D , individual 4 with a CI value of 50 is found and removed. In  FIG. 3E , individual 1 with a CI value of 24 is found and removed. In  FIG. 3F , individual 3 with a CI value of 12 is found and removed. In  FIG. 3G , individual 2 with a CI value of 4 is found and removed. In  FIG. 3H , individual 15 with a CI value of 1 is found and removed. In  FIG. 3I , the remaining individuals have a CI value of zero indicating those individuals are not targeted in the marketing campaign. 
     In one embodiment, the method outputs a rank order with regard to influential individuals within the social network. For example, in the embodiment of  FIGS. 3A to 3I , the rank order is individuals  19 ,  7 ,  4 ,  1 ,  3 ,  2  and  15 . 
     To further investigate the applicability of the CI method in real large-scale social network, a social contact network built from the mobile phone calls between people in Mexico is considered. A mobile phone call social network reflects people&#39;s interactions in social lives, and represents a proxy of a human contact network. In order to build the network, a link between two people is established if there is a reciprocal phone call between them in an observation window of three months (i.e. a call in both directions), and the number of such reciprocal calls is larger than or equal to three. This criterion gives a network of N=14, 346, 653 people, with an average degree &lt;k&gt;=3.53 and a maximum degree k max =419. The phone call network is the prototype of big-data, where a scalable (i.e. almost linear) method, such as the CI method, is mandatory. The result of the CI method, compared to HDA, PAGERANK®, HD and k-core, is shown in  FIG. 2B . CI is better by a very good margin. Indeed, it fragments the network using about 500,000 people less than the best heuristic strategy (HDA). 
     As shown in  FIG. 2A  and  FIG. 2B  the CI method is compared with Degree Centrality (HD), Adaptive Degree Centrality (HDA), PAGERANK® (PR) and k-core methods. Two real-world networks are used TWITTER® ( FIG. 2A ) and Phone Calls ( FIG. 2B ) to test the resilience of these networks if the most influential nodes are removed from the network. Y-axis represents the size of the largest connected component and X-axis represents the fraction of nodes removed from the network using one of methods. CI clearly outperforms all other methods in identifying influential nodes responsible of keeping the entire network connected. For example, in  FIG. 2A , the CI method identifies a minimum number of influential nodes (q less than 0.06) to fragment the network (G=0). In contrast, HDA required more nodes (q of about 0.09) to fragment the network while HD required even more nodes (q of about 0.1) and PAGERANK® is even less optimal. Likewise, in  FIG. 2B , the CI method identifies a minimum number of influential nodes (q of about 0.08) to fragment the network (G=0). HDA (q of about 0.11) and HD and PAGERANK® (q of about 0.12) required more nodes to fragment the network. This demonstrates the CI method can identify key nodes more effectively than either the HDA or HD and PAGERANK® methods. 
     As shown  FIG. 4A  and  FIG. 4B , the disclosed method was also tested on two synthetic networks, a random Erdos-Renyi network and a scale free network. Again the results clearly show that the disclosed CI method is more efficient as compared to HDA, PAGERANK® and HD methods. Two synthetic networks are used: Random Network—Erdos Renyi ( FIG. 2A ) and Scale Free network ( FIG. 2B ) to test the methods. Y-axis represents the size of the largest connected component and X-axis represents the fraction of nodes removed from the network using one of methods. CI clearly outperforms all other strategies in identifying influential nodes responsible of keeping the entire network connected. 
     In general, the disclosed method assigns a ranking of influence in a social network. The method to assign this ranking is based on the contact information of a network. The method takes as input all the links of a network and assigns a rank to all the nodes on the basis of collective behavior. Examples of the types of social networks include phone call records in a mobile network, friendship-links or any kind of interaction-link between people in online social networks such as mentions and retweets in a TWITTER® network. The method is used to optimally place ads in a mobile network or social network, such as TWITTER® or FACEBOOK®. When the network structure is obtained, the disclosed CI method is used to find the minimal set of most influential people in social networks to be targeted in an advertisement campaign. 
     The disclosed method may be applied to a variety of networks and complex systems emerging from a number of different scientific fields. A non-exhaustive list of applications includes (1) devising strategies to increase robustness of electrical power grids across the country foreseeing possible targeted terrorist attacks or natural disaster (2) developing immunization strategies against possible virus outbreak of infectious diseases and (3) identification of weakly connected nodes in computer networks whose removal can cause global network failure. 
     As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method, or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.), or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “service,” “circuit,” “circuitry,” “module,” and/or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a non-transient computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code and/or executable instructions embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code may execute entirely on the user&#39;s computer (device), partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). 
     Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.