Descriptive Analysis of Network Graph Characteristics

In the study of a given complex system, questions of interest can often be re-phrased in a useful manner as questions regarding some aspect of the structure or characteristics of a corresponding network graph. For example, various types of basic social dynamics can be represented by triplets of vertices with a particular pattern of ties among them (i.e., triads ); questions involving the movement of information or commodities usually can be posed in terms of paths on the network graph and flows along those paths; certain notions of the ‘importance’ of individual system elements may be captured by measures of how ‘central’ the corresponding vertex is in the network; and the search for ‘communities’ and analogous types of unspecified ‘groups’ within a system frequently may be addressed as a graph partitioning problem.

[1]  P. Holland,et al.  A Method for Detecting Structure in Sociometric Data , 1970, American Journal of Sociology.

[2]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[3]  M. Newman,et al.  Finding community structure in networks using the eigenvectors of matrices. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Andrea Lancichinetti,et al.  Community detection algorithms: a comparative analysis: invited presentation, extended abstract , 2009, VALUETOOLS.

[5]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data , 2009 .

[6]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994 .

[7]  Eric D. Kolaczyk,et al.  Statistical Analysis of Network Data: Methods and Models , 2009 .

[8]  Lada A. Adamic,et al.  Friends and neighbors on the Web , 2003, Soc. Networks.

[9]  B. Mohar.  THE LAPLACIAN SPECTRUM OF GRAPHS y , 1991 .

[10]  Ulrik Brandes,et al.  Network Analysis: Methodological Foundations (Lecture Notes in Computer Science) , 2005 .

[11]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[12]  M. Newman,et al.  Mixing patterns in networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  P. Bonacich.  Factoring and weighting approaches to status scores and clique identification , 1972 .

[14]  John Scott.  Social Network Analysis , 1988 .

[15]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[16]  Leonard M. Freeman,et al.  A set of measures of centrality based upon betweenness , 1977 .

[17]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[18]  M. Newman,et al.  Finding community structure in very large networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[20]  Croom Helm,et al.  Data Source: Scott, J. (1991). Social network analysis: A handbook. Newbury Park, California: SAGE Publications. , 1991 .

[21]  John Skvoretz,et al.  Node centrality in weighted networks: Generalizing degree and shortest paths , 2010, Soc. Networks.

[22]  Ulrik Brandes,et al.  Network Analysis: Methodological Foundations , 2010 .

[23]  Gert Sabidussi,et al.  The centrality index of a graph , 1966 .

[24]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Jon Kleinberg,et al.  Authoritative sources in a hyperlinked environment , 1999, SODA '98.

[26]  Anil K. Jain,et al.  Data clustering: a review , 1999, CSUR.

[27]  Leo Katz,et al.  A new status index derived from sociometric analysis , 1953 .

[28]  S. Leinhardt,et al.  The Structure of Positive Interpersonal Relations in Small Groups. , 1967 .