The investigation of community structures in networks is an important issue in many domains and disciplines. This problem is relevant for social tasks (objective analysis of relationships on the web), biological inquiries (functional studies in metabolic and protein networks), or technological problems (optimization of large infrastructures). Several types of algorithms exist for revealing the community structure in networks, but a general and quantitative definition of community is not implemented in the algorithms, leading to an intrinsic difficulty in the interpretation of the results without any additional nontopological information. In this article we deal with this problem by showing how quantitative definitions of community are implemented in practice in the existing algorithms. In this way the algorithms for the identification of the community structure become fully self-contained. Furthermore, we propose a local algorithm to detect communities which outperforms the existing algorithms with respect to computational cost, keeping the same level of reliability. The algorithm is tested on artificial and real-world graphs. In particular, we show how the algorithm applies to a network of scientific collaborations, which, for its size, cannot be attacked with the usual methods. This type of local algorithm could open the way to applications to large-scale technological and biological systems.

We study numerically the ordering process of two very simple dynamical models for a two-state variable on several topologies with increasing levels of heterogeneity in the degree distribution. We find that the zero-temperature Glauber dynamics for the Ising model may get trapped in sets of partially ordered metastable states even for finite system size, and this becomes more probable as the size increases. Voter dynamics instead always converges to full order on finite networks, even if this does not occur via coherent growth of domains. The time needed for order to be reached diverges with the system size. In both cases the ordering process is rather insensitive to the variation of the degree distribution from sharply peaked to scale free.

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A cellular automata model is used to study aspects of cultural change in spatial environments. Cultures are represented as bit strings in individual cells. Cultures may change because they become more similar to prevailing nearby cultures, are subject to intrinsic random changes, or expand to previously empty cells. Extending Axelrod's (1997) results, the authors show that assimilation does not lead to a single homogeneous culture even if, unlike in Axelrod's model, cultural assimilation may take place even between neighboring cells with zero similarity; intrinsic changes decrease rather than increase the number of stable cultural regions; and expansion of a single culture in a previously unoccupied territory does not result in a single culture in the entire territory. Geographical features (such as mountains) that are an obstacle to contact between cells increase the number of different cultural regions.Culture is behaviors, languages, beliefs, attitudes, and values that individuals learn from other individuals (Cavalli-Sforza and Feldmann 1981;Boyd and Richerson 1985). Every human group has its own distinctive culture, but the cultures of human groups in reciprocal contact tend to become more similar because individuals in one group may learn some of their behaviors, languages, beliefs, attitudes, and values from individuals in other groups with which they interact. One would then predict that if a territory contains several human groups, each with its own distinctive culture, but with neighboring groups interacting, given enough time, there will be only a single homogeneous culture in the entire territory. Using a simple simulation model, Axelrod (1997) has shown that this is not so. Starting from an initial condition in which the cultures of the human groups existing in a territory are randomly generated and therefore tend to be all different, there is, in fact, a process of progressive cultural 163 AUTHORS' NOTE: The computer simulations routines used in this article can be found at

Abstract. In this paper the results of several agent-based simulations, aiming to test the role of normative beliefs in the emergence and innovation of social norms, are presented and discussed. Rather than mere behavioral regularities, norms are here seen as behaviors spreading to the extent that and because the corresponding commands and beliefs do spread as well. On the grounds of such a view, the present work will endeavour to show that a sudden external constraint (e.g. a barrier preventing agents from moving among social settings) facilitates norm innovation: under such a condition, agents provided with a module for telling what a norm is can generate new (social) norms by forming new normative beliefs, irrespective of the most frequent actions.