Many popular measures used in social network analysis, including centrality, are based on the random walk. The random walk is a model of a stochastic process where a node interacts with one other node at a time. However, the random walk may not be appropriate for modeling social phenomena, including epidemics and information diffusion, in which one node may interact with many others at the same time, for example, by broadcasting the virus or information to its neighbors. To produce meaningful results, social network analysis algorithms have to take into account the nature of interactions between the nodes. In this paper we classify dynamical processes as conservative and non-conservative and relate them to well-known measures of centrality used in network analysis: PageRank and Alpha-Centrality. We demonstrate, by ranking users in online social networks used for broadcasting information, that non-conservative Alpha-Centrality generally leads to a better agreement with an empirical ranking scheme than the conservative PageRank.
@cite_28 studied measures similar to Alpha-Centrality and personalized PageRank (with attenuation factor 1) which they call communicability. They linked the communicability functions to dynamics by showing their relationship to the thermal Green's function of oscillators. They used communicability to identify important actors in small social networks, demonstrating that different communicability functions led to different judgements of centrality, but did not justify the choice of the particular communicability function in terms of the interactions taking place between actors. Although we study a similar function, the goal of our work is to contrast conservative and non-conservative dynamics and explain how these differences should guide the choice of centrality measure for a given social network.
@cite_28
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Abstract A fundamental problem in the study of complex networks is to provide quantitative measures of correlation and information flow between different parts of a system. To this end, several notions of communicability have been introduced and applied to a wide variety of real-world networks in recent years. Several such communicability functions are reviewed in this paper. It is emphasized that communication and correlation in networks can take place through many more routes than the shortest paths, a fact that may not have been sufficiently appreciated in previously proposed correlation measures. In contrast to these, the communicability measures reviewed in this paper are defined by taking into account all possible routes between two nodes, assigning smaller weights to longer ones. This point of view naturally leads to the definition of communicability in terms of matrix functions, such as the exponential, resolvent, and hyperbolic functions, in which the matrix argument is either the adjacency matrix or the graph Laplacian associated with the network. Considerable insight on communicability can be gained by modeling a network as a system of oscillators and deriving physical interpretations, both classical and quantum-mechanical, of various communicability functions. Applications of communicability measures to the analysis of complex systems are illustrated on a variety of biological, physical and social networks. The last part of the paper is devoted to a review of the notion of locality in complex networks and to computational aspects that by exploiting sparsity can greatly reduce the computational efforts for the calculation of communicability functions for large networks. The total communicability of a network (or graph) is defined as the sum of the entries in the exponential of the adjacency matrix of the network, possibly normalized by the number of nodes. This quantity offers a good measure of how easily information spreads across the network, and can be useful in the design of networks having certain desirable properties. The total communicability can be computed quickly even for large networks using techniques based on the Lanczos algorithm. In this work we introduce some heuristics that can be used to add, delete, or rewire a limited number of edges in a given sparse network so that the modified network has a large total communicability. To this end, we introduce new edge centrality measures, which can be used as a guide in the selection of edges to be added or removed. Moreover, we show experimentally that the total communicability provides an effective and easily computable measure of how "well-connected" a sparse network is. We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we describe fast and effective criteria for the selection of edges to be added to (or deleted from) a given directed network so as to enhance these network communicability measures. Numerical experiments illustrate the effectiveness of the proposed techniques. Degree centrality is considered to be one of the most basic measures of social network analysis, which has been used extensively in diverse research domains for measuring network positions of actors in respect of the connections with their immediate neighbors. In network analysis, it emphasizes the number of connections that an actor has with others. However, it does not accommodate the value of the duration of relations with other actors in a network; and, therefore, this traditional degree centrality approach regards only the presence or absence of links. Here, we introduce a time-variant approach to the degree centrality measure — time scale degree centrality (TSDC), which considers both presence and duration of links among actors within a network. We illustrate the difference between traditional and TSDC measure by applying these two approaches to explore the impact of degree attributes of a patient-physician network evolving during patient hospitalization periods on the hospital length of stay (LOS) both at a macro- and a micro-level. At a macro-level, both the traditional and time-scale approaches to degree centrality can explain the relationship between the degree attribute of the patient-physician network and LOS. However, at a micro-level or small cluster level, TSDC provides better explanation while the traditional degree centrality approach is found to be inadequate in explaining its relationship with LOS. Our proposed TSDC measure can explore time-variant relations that evolve among actors in a given social network. Several centrality measures have been formulated to quantify the notion of 'importance' of actors in social networks. Current measures scrutinize either local or global connectivity of the nodes and have been found to be inadequate for social networks. Ignoring hierarchy and community structure, which are inherent in all human social networks, is the primary cause of this inadequacy. Positional hierarchy and embeddedness of an actor in the community are intuitively crucial determinants of his importance. The theory of social capital asserts that an actor's importance is derived from his position in network hierarchy as well as from the potential to mobilize resources through intra-community (bonding) and inter-community (bridging) ties. Inspired by this idea, we propose a novel centrality measure SC (Social Centrality) for actors in social networks. Our measure accounts for - i) an individual's propensity to socialize, and ii) his connections within and outside the community. These two factors are suitably aggregated to produce social centrality score. Comparative analysis of SC measure with classical and recent centrality measures using large public networks shows that it consistently produces a more realistic ranking of nodes. The inference is based on the available ground truth for each tested networks. Extensive analysis of rankings delivered by SC measure and mapping with known facts in well-studied networks justifies its effectiveness in diverse social networks. Scalability evaluation of SC measure justifies its efficacy for real-world large networks. Summary Background Strong evidence shows that physical inactivity increases the risk of many adverse health conditions, including major non-communicable diseases such as coronary heart disease, type 2 diabetes, and breast and colon cancers, and shortens life expectancy. Because much of the world's population is inactive, this link presents a major public health issue. We aimed to quantify the effect of physical inactivity on these major non-communicable diseases by estimating how much disease could be averted if inactive people were to become active and to estimate gain in life expectancy at the population level. Methods For our analysis of burden of disease, we calculated population attributable fractions (PAFs) associated with physical inactivity using conservative assumptions for each of the major non-communicable diseases, by country, to estimate how much disease could be averted if physical inactivity were eliminated. We used life-table analysis to estimate gains in life expectancy of the population. Findings Worldwide, we estimate that physical inactivity causes 6 (ranging from 3·2 in southeast Asia to 7·8 in the eastern Mediterranean region) of the burden of disease from coronary heart disease, 7 (3·9–9·6) of type 2 diabetes, 10 (5·6–14·1) of breast cancer, and 10 (5·7–13·8) of colon cancer. Inactivity causes 9 (range 5·1–12·5) of premature mortality, or more than 5·3 million of the 57 million deaths that occurred worldwide in 2008. If inactivity were not eliminated, but decreased instead by 10 or 25 , more than 533 000 and more than 1·3 million deaths, respectively, could be averted every year. We estimated that elimination of physical inactivity would increase the life expectancy of the world's population by 0·68 (range 0·41–0·95) years. Interpretation Physical inactivity has a major health effect worldwide. Decrease in or removal of this unhealthy behaviour could improve health substantially. Funding None. Abstract A new family of centrality measures, based on game theoretical concepts, is proposed for social networks. To reflect the interests that motivate the interactions among individuals in a network, a cooperative game in characteristic function form is considered. From the graph and the game, the graph-restricted game is obtained. Shapley value in a game is considered as actor’s power. The difference between actor’s power in the new game and his her power in the original one is proposed as a centrality measure. Conditions are given to reach some desirable properties. Finally, a decomposition is proposed. Who are the influential people in an online social network? The answer to this question depends not only on the structure of the network, but also on details of the dynamic processes occurring on it. We classify these processes as conservative and non-conservative. A random walk on a network is an example of a conservative dynamic process, while information spread is non-conservative. The influence models used to rank network nodes can be similarly classified, depending on the dynamic process they implicitly emulate. We claim that in order to correctly rank network nodes, the influence model has to match the details of the dynamic process. We study a real-world network on the social news aggregator Digg, which allows users to post and vote for news stories. We empirically define influence as the number of in-network votes a user's post generates. This influence measure, and the resulting ranking, arises entirely from the dynamics of voting on Digg, which represents non-conservative information flow. We then compare predictions of different influence models with this empirical estimate of influence. The results show that non-conservative models are better able to predict influential users on Digg. We find that normalized alpha-centrality metric turns out to be one of the best predictors of influence. We also present a simple algorithm for computing this metric and the associated mathematical formulation and analytical proofs. A simple deterministic algorithm for community detection is provided by using two rounds of minimum spanning trees. By comparing the first round minimum spanning tree (1st-MST) with the second round spanning tree (2nd-MST) of the network, communities are detected and their overlapping nodes are also identified. To generate the two MSTs, a distance matrix is defined and computed from the adjacent matrix of the network. Compared with the resistance matrix or the communicability matrix used in community detection in the literature, the proposed distance matrix is very simple in computation. The proposed algorithm is tested on real world social networks, graphs which are failed by the modularity maximization, and the LFR benchmark graphs for community detection. The study of the topological structure of complex networks has fascinated researchers for several decades, and today we have a fairly good understanding of the types and reoccurring characteristics of many different complex networks. However, surprisingly little is known today about models to compare complex graphs, and quantitatively measure their similarity. This paper proposes a natural similarity measure for complex networks: centrality distance, the difference between two graphs with respect to a given node centrality. Centrality distances allow to take into account the specific roles of the different nodes in the network, and have many interesting applications. As a case study, we consider the closeness centrality in more detail, and show that closeness centrality distance can be used to effectively distinguish between randomly generated and actual evolutionary paths of two dynamic social networks. In this paper, we introduce a time-variant approach to degree centrality measure - time scale degree centrality (TSDC), which considers both presence and duration of links among actors within a network, whereas, the traditional degree centrality approach regards only the presence or absence of links. We illustrate the difference between traditional and time scale degree centrality measure by applying these two approaches to explore the impact of 'degree' attributes of doctor-patient network that evolves during patient hospitalization period on the hospital length of stay (LOS) both in macro- and micro-level. In macro-level, both the traditional and time-scale approaches to degree centrality can explain the relationship between the 'degree' attribute of doctor-patient network and LOS. However, at micro-level or small cluster level, TSDC provides better explanation while traditional degree centrality approach is impotent to explain the relationship between them. Motivation: Discovering and understanding patterns in networks of protein–protein interactions (PPIs) is a central problem in systems biology. Alignments between these networks aid functional understanding as they uncover important information, such as evolutionary conserved pathways, protein complexes and functional orthologs. A few methods have been proposed for global PPI network alignments, but because of NP-completeness of underlying sub-graph isomorphism problem, producing topologically and biologically accurate alignments remains a challenge. Results: We introduce a novel global network alignment tool, Lagrangian GRAphlet-based ALigner (L-GRAAL), which directly optimizes both the protein and the interaction functional conservations, using a novel alignment search heuristic based on integer programming and Lagrangian relaxation. We compare L-GRAAL with the state-of-the-art network aligners on the largest available PPI networks from BioGRID and observe that L-GRAAL uncovers the largest common sub-graphs between the networks, as measured by edge-correctness and symmetric sub-structures scores, which allow transferring more functional information across networks. We assess the biological quality of the protein mappings using the semantic similarity of their Gene Ontology annotations and observe that L-GRAAL best uncovers functionally conserved proteins. Furthermore, we introduce for the first time a measure of the semantic similarity of the mapped interactions and show that L-GRAAL also uncovers best functionally conserved interactions. In addition, we illustrate on the PPI networks of baker's yeast and human the ability of L-GRAAL to predict new PPIs. Finally, L-GRAAL's results are the first to show that topological information is more important than sequence information for uncovering functionally conserved interactions. Availability and implementation: L-GRAAL is coded in C++. Software is available at: http: bio-nets.doc.ic.ac.uk L-GRAAL . Contact: ku.ca.lairepmi@ningod-dolam.n Supplementary information: Supplementary data are available at Bioinformatics online. Three measures of actors' network centrality are derived from an elementary rocess model of social influence. The measures are closely related to, and cast new light on, widely used measures of actors' centrality; for example, the essential social organization of status that has been assumed by Hubbell, Bonacich, Coleman, and Burt appears as a deducible outcome of this social influence process. Unlike previous measures, which have been viewed as competing alternatives, the present measures are complementary and, in their juxtaposition, provide for a rich description of social structure. The complementary indicates a degree of theoretical unification in the work on network centrality that was heretofore unsuspected. For a long time now, researchers have worked on defining different metrics able to characterize the importance of nodes in networks. Among them, centrality measures have proved to be pertinent as they relate the position of a node in the structure to its ability to diffuse an information efficiently. The case of dynamic networks, in which nodes and links appear and disappear over time, led the community to propose extensions of those classical measures. Yet, they do not investigate the fact that the network structure evolves and that node importance may evolve accordingly. In the present paper, we propose temporal extensions of notions of centrality, which take into account the paths existing at any given time, in order to study the time evolution of nodes' importance in dynamic networks. We apply this to two datasets and show that the importance of nodes does indeed vary greatly with time. We also show that in some cases it might be meaningless to try to identify nodes that are consistently important over time, thus strengthening the interest of temporal extensions of centrality measures. The massive presence of silent members in online communities, the so-called lurkers, has long attracted the attention of researchers in social science, cognitive psychology, and computer-human interaction. However, the study of lurking phenomena represents an unexplored opportunity of research in data mining, information retrieval and related fields. In this paper, we take a first step towards the formal specification and analysis of lurking in social networks. Particularly, focusing on the network topology, we address the new problem of lurker ranking and propose the first centrality methods specifically conceived for ranking lurkers in social networks. Using Twitter and FriendFeed as cases in point, our methods' performance was evaluated against data-driven rankings as well as existing centrality methods, including the classic PageRank and alpha-centrality. Empirical evidence has shown the significance of our lurker ranking approach, which substantially differs from other methods in effectively identifying and ranking lurkers. Identifying and removing spurious links in complex networks is meaningful for many real applications and is crucial for improving the reliability of network data, which, in turn, can lead to a better understanding of the highly interconnected nature of various social, biological, and communication systems. In this paper, we study the features of different simple spurious link elimination methods, revealing that they may lead to the distortion of networks’ structural and dynamical properties. Accordingly, we propose a hybrid method that combines similarity-based index and edge-betweenness centrality. We show that our method can effectively eliminate the spurious interactions while leaving the network connected and preserving the network's functionalities. In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the state-space model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a time-evolving mixed membership vector that allows actors to behave differently over time and carry out different roles functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson's network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors. The massive presence of silent members in online communities, the so-called lurkers, has long attracted the attention of researchers in social science, cognitive psychology, and computer–human interaction. However, the study of lurking phenomena represents an unexplored opportunity of research in data mining, information retrieval and related fields. In this paper, we take a first step towards the formal specification and analysis of lurking in social networks. We address the new problem of lurker ranking and propose the first centrality methods specifically conceived for ranking lurkers in social networks. Our approach utilizes only the network topology without probing into text contents or user relationships related to media. Using Twitter, Flickr, FriendFeed and GooglePlus as cases in point, our methods’ performance was evaluated against data-driven rankings as well as existing centrality methods, including the classic PageRank and alpha-centrality. Empirical evidence has shown the significance of our lurker ranking approach, and its uniqueness in effectively identifying and ranking lurkers in an online social network. A complex network can be modeled as a graph representing the ''who knows who'' relationship. In the context of graph theory for social networks, the notion of centrality is used to assess the relative importance of nodes in a given network topology. For example, in a network composed of large dense clusters connected through only a few links, the nodes involved in those links are particularly critical as far as the network survivability is concerned. This may also impact any application running on top of it. Such information can be exploited for various topological maintenance issues to prevent congestion and disruption. This can also be used offline to identify the most important actors in large social interaction graphs. Several forms of centrality have been proposed so far. Yet, they suffer from imperfections: initially designed for small social graphs, they are either of limited use (degree centrality), either incompatible in a distributed setting (e.g. random walk betweenness centrality). In this paper we introduce a novel form of centrality: the second order centrality which can be computed in a distributed manner. This provides locally each node with a value reflecting its relative criticity and relies on a random walk visiting the network in an unbiased fashion. To this end, each node records the time elapsed between visits of that random walk (called return time in the sequel) and computes the standard deviation (or second order moment) of such return times. The key point is that central nodes see regularly the random walk compared to other topology nodes. Both through theoretical analysis and simulation, we show that the standard deviation can be used to accurately identify critical nodes as well as to globally characterize graphs topology in a distributed way. We finally compare our proposal to well-known centralities to assess its competitivity. The ability to measure centrality in social networks has been a particularly useful development in social network analysis. For researchers trying to decide which centrality measure is most meaningful and valid for their research purposes, various papers have explored the conceptual foundations of centrality measures. Less well documented is the empirical performance of centrality measures under different research scenarios or constraints. This study uses bootstrap sampling procedures to determine how sampling affects the stability of 11 different network centrality measures. Results indicate that some measures are more stable than others, and that stability is also a function of network and study properties.