The "new" science of networks

Queries on the paper:
Watts, D.J. (2004) The "new" science of networks, Annual Review of Sociology 30: 243-270

In this paper, Watts reviews recent research in what he called the "new" science of networks. The network models he discussed have drawn a remarkable attention because these models reveal several interesting common patterns that can be observed in a variety of empirical networks. The small-world model proposed by Watts and Strogatz simulates a highly clustered network with short average paths, indicating that even few random shortcuts can lead to significant changes in transmitting message within the networks. The scale-free networks, characterized by power-law degree distribution, embody the mechanisms of population growth and preferential attachment that are widely observable. Inspired by these models, many researches in different disciplines have uncovered more generalized network properties or dynamics.

Watts argues that the family of the researches is new because it often deals with enormous amount of empirical data that requires high computing power and highly interdisciplinary synthesis of new analytical techniques. This argument is not sufficient to emphasize the importance of such research direction. For me, it is new because it suggests a new way to look at the connection between a pure scientific model and an "organic system". For mathematical scientists, the network properties characterized by certain metrics would be able to explain the social or biological phenomena. For researcher from other disciplines such as social scientists and biologists, the seemingly complex and puzzling phenomena can possibly be formulated in computational models.

While recognizing the importance of the new network research, at least some concerns have come into my mind:
1. How to characterize a network?
Prior network models and empirical data analysis generally focus on measures of degree and distance distribution, which cannot sufficiently characterize the network properties. For example, in scale-free networks, the metric of average path length are not informative enough because a path containing a hub (a node with extremely high degrees) functions distinctively in transmitting messages. Therefore, proposing proper metrics for different networks is needed.
2. The semantics of links
Most of the generative or analytical models focus on either the global link structure or local connection information in the graph-represented networks and overlook the fact that most empirical networks are the consequence of individuals’ action and interaction. Thus the links can have different semantics depending on the context of its use. Discovering the semantics of links would help clarify the rational of individuals’ action/interaction so that we can construct more reasonable generative models or refine the network analysis.
3. Temporal dynamics and external triggers
Most empirical networks are not static graphs but with highly temporal dynamics. Some proposed models, such as the scale-free model, have considered the temporal nature of networks. However, the real-world networks usually form and evolve corresponding to the external or global events, which are very different from the self-contained, modeling networks. A proper model or representation of external triggers would be crucial to understand the network dynamics.