text: Methods to solve a node discovery problem for a social network are presented. Covert nodes refer to the nodes which are not observable directly. They transmit the influence and affect the resulting collaborative activities among the persons in a social network, but do not appear in the surveillance logs which record the participants of the collaborative activities. Discovering the covert nodes is identifying the suspicious logs where the covert nodes would appear if the covert nodes became overt. The performance of the methods is demonstrated with a test dataset generated from computationally synthesized networks and a real organization.
  @cite_9: 
  @cite_0: This paper generalizes thep* class of models for social network data to predict individual-level attributes from network ties. Thep* model for social networks permits the modeling of social relationships in terms of particular local relational or network configurations. In this paper we present methods for modeling attribute measures in terms of network ties, and so constructp* models for the patterns of social influence within a network. Attribute variables are included in a directed dependence graph and the Hammersley-Clifford theorem is employed to derive probability models whose parameters can be estimated using maximum pseudo-likelihood. The models are compared to existing network effects models. They can be interpreted in terms of public or private social influence phenomena within groups. The models are illustrated by an empirical example involving a training course, with trainees' reactions to aspects of the course found to relate to those of their network partners.
  @cite_23: This paper generalizes thep* model for dichotomous social network data (Wasserman & Pattison, 1996) to the polytomous case. The generalization is achieved by transforming valued social networks into three-way binary arrays. This data transformation requires a modification of the Hammersley-Clifford theorem that underpins thep* class of models. We demonstrate that, provided that certain (non-observed) data patterns are excluded from consideration, a suitable version of the theorem can be developed. We also show that the approach amounts to a model for multiple logits derived from a pseudo-likelihood function. Estimation within this model is analogous to the separate fitting of multinomial baseline logits, except that the Hammersley-Clifford theorem requires the equating of certain parameters across logits. The paper describes how to convert a valued network into a data array suitable for fitting the model and provides some illustrative empirical examples.
  @cite_2: Abstract A major criticism of the statistical models for analyzing social networks developed by Holland, Leinhardt, and others [Holland, P.W., Leinhardt, S., 1977. Notes on the statistical analysis of social network data; Holland, P.W., Leinhardt, S., 1981. An exponential family of probability distributions for directed graphs. Journal of the American Statistical Association. 76, pp. 33–65 (with discussion); Fienberg, S.E., Wasserman, S., 1981. Categorical data analysis of single sociometric relations. In: Leinhardt, S. (Ed.), Sociological Methodology 1981, San Francisco: Jossey-Bass, pp. 156–192; Fienberg, S.E., Meyer, M.M., Wasserman, S., 1985. Statistical analysis of multiple sociometric relations. Journal of the American Statistical Association, 80, pp. 51–67; Wasserman, S., Weaver, S., 1985. Statistical analysis of binary relational data: Parameter estimation. Journal of Mathematical Psychology. 29, pp. 406–427; Wasserman, S., 1987. Conformity of two sociometric relations. Psychometrika. 52, pp. 3–18] is the very strong independence assumption made on interacting individuals or units within a network or group. This limiting assumption is no longer necessary given recent developments on models for random graphs made by Frank and Strauss [Frank, O., Strauss, D., 1986. Markov graphs. Journal of the American Statistical Association. 81, pp. 832–842] and Strauss and Ikeda [Strauss, D., Ikeda, M., 1990. Pseudolikelihood estimation for social networks. Journal of the American Statistical Association. 85, pp. 204–212]. The resulting models are extremely flexible and easy to fit to data. Although Wasserman and Pattison [Wasserman, S., Pattison, P., 1996. Logit models and logistic regressions for social networks: I. An introduction to Markov random graphs and p*. Psychometrika. 60, pp. 401–426] present a derivation and extension of these models, this paper is a primer on how to use these important breakthroughs to model the relationships between actors (individuals, units) within a single network and provides an extension of the models to multiple networks. The models for multiple networks permit researchers to study how groups are similar and or how they are different. The models for single and multiple networks and the modeling process are illustrated using friendship data from elementary school children from a study by Parker and Asher [Parker, J.G., Asher, S.R., 1993. Friendship and friendship quality in middle childhood: Links with peer group acceptance and feelings of loneliness and social dissatisfaction. Developmental Psychology. 29, pp. 611–621].
  @cite_25: Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes in power-law graphs and that have costs scaling sublinearly with the size of the graph. We also demonstrate the utility of these strategies on the GNUTELLA peer-to-peer network.
  @cite_12: We argue that social networks can be modeled as the outcome of processes that occur in overlapping local regions of the network, termed local social neighborhoods. Each neighborhood is conceived as a possible site of interaction and corresponds to a subset of possible network ties. In this paper, we discuss hypotheses about the form of these neighborhoods, and we present two new and theoretically plausible ways in which neighborhood-based models for networks can be constructed. In the first, we introduce the notion of a setting structure, a directly hypothesized (or observed) set of exogenous constraints on possible neighborhood forms. In the second, we propose higher-order neighborhoods that are generated, in part, by the outcome of interactive network processes themselves. Applications of both approaches to model construction are presented, and the developments are considered within a general conceptual framework of locale for social networks. We show how assumptions about neighborhoods can be cast with...
  @cite_17: 
summary: Markov random network is a model of the joint probability distribution of random variables. It is an undirected graphical model similar to a Bayesian network. The Markov random network is used to learn the dependency between the links which shares a node. The Markov random network is one of the dependence graphs @cite_17 , which models the dependency between links. Extension to hierarchical models @cite_25 , multiple networks (treating different types of relationships) @cite_9 , valued networks (with nodal attributes) @cite_23 , higher order dependency between the links which share no nodes @cite_12 , and 2-block chain graphs (associating one set of explanatory variables with the other set of outcome variables) @cite_0 are studied. A family of such extensions and model elaborations is named the exponential random graph @cite_2 .