The purpose of this tutorial will be to discuss the basic features of scale-free networks, from empirical data to growth models and consequences.

In this talk, we will present the basic methods for the analysis of the clustering and the detection of communities in networks. We also present an application of these methods to the case of a word association network and to the case of wikipedia.

The changes looming in the organizational landscape signal the need for a new generation of organizational theory and research that responds to the assumptions, aspirations, and adversities that will characterize these 21st century organizational forms. While there has been a long-standing interest in the study of organizations from a social network perspective the fundamental changes outlined above suggest that the research agenda needs to evolve from studying networks in (or between) organizations to grapple with the notion that the network is the organization. This nuanced, yet significant, change in perspective has substantial -- and substantive -- implications for the deployment of a comprehensive network analytic framework to specify and statistically model the structural tendencies of network forms on the bases of multiple theories and at multiple levels of analyses (Contractor, Wasserman, & Faust, 2006; Monge & Contractor, 2003). Towards that goal, this tutorial begins by reviewing some of the theoretical and methodological accomplishments and challenges of contemporary research on networks. Next the tutorial offers an analytic framework that can be used to specify and statistically test simultaneously multilevel multi-theoretical hypotheses about the structural tendencies of networks. The tutorial concludes with an empirical study that illustrates some of the capabilities of this framework.

Ecologists have a long history of studying food webs, the networks of feeding relationships among species, as demonstrated by the work of Charles Elton in the 1920's. The current focus on integrated empiricism, analysis and modeling was kick-started by mathematical analyses of community stability published by Robert May in 1973. In this tutorial, I will discuss the history of food-web concepts and research, current key topics with an emphasis on the structure and dynamics of complex food webs, and how such work fits within the broader framework of network research.

First, I will discuss the simplest synchronization paradigm in a noisy environment, the Edwards-Wilkinson process on an arbitrary network. I will specifically consider the problem of optimizing synchronization in weighted complex networks with fixed total edge cost. Then, employing recent connections between the Edwards-Wilkinson process and resistor networks, and some well-known connections between random walks and resistor networks, I will also pursue a naturally related problem of optimizing performance in queue-limited communication networks utilizing local weighted random "routing" schemes. I will discuss two methods for studying the above problems: exact numerical diagonalization and mean-field approximation on uncorrelated network, http://arxiv.org/abs/cond-mat/0609098.

In the first part of my talk I will describe the common topological properties of genome-wide protein binding networks such as their broad degree distribution, a particular set of degree-degree correlations, and a heavily interconnected "small-world" topology. Then I will introduce and compare different models proposed to account for their appearance: 1) The evolutionary explanation using growth models in which the network grows y duplication of individual genes 2) The biophysical explanation based on a broad distribution of "stickiness" of individual proteins. 3) The functional explanation: there are just as many binding partners of a given protein as needed for its function and these functional requirements are very heterogeneous. In the second part of my talk I will go beyond pure topological description and look at the Law of Mass Action (LMA) equilibrium of reversible protein binding networks and the kinetics of its response to perturbations in abundances of individual proteins. I will demonstrate that the extent of changes in free and bound concentrations of both immediate and more distant neighbors of a perturbed protein is influenced by such factors as the network topology, the distribution of protein abundances among its nodes, and the average binding strength.

A will briefly introduce the notion of gradient networks and discuss its implications on the collective efficiency of social networks in competitive environments.