Small Worlds: The Dynamics of Networks between Order and Randomness

The Cohesiveness of Blocks In Social Networks: Node Connectivity and Conditional Density

“…It is clear that cohesion is an important concept fundamental to defining social groups and their boundaries as emergent phenomena. Work carried out by Watts (1999aWatts ( ,1999b on the small world problem tied network structure to an important global characteristic of networks, their "connectedness," but like Wasserman and Faust (1994:115-17) he did not utilize the graph theoretic measurement of connectivity. 43 Small-scale "social psychological" cohesion based on the model of cliques and attachment-to-group makes a difference because social psychological cohesion affects the strength of group norms, how much individuals are willing to sacrifice for the groups, and so forth.…”

“…Within a social group, high connectivity plus a modest additional density of randomly distributed ties that reduce average path length within the group (Watts 1999b) is capable of generating large-scale group cohesion, as we showed in Section I.D. Our hypotheses (I.B) suggested how such cohesion might affect coordinated social action, social homogeneity, the emergence of group norms at the macro level and, in sufficiently compact groups (I.C), the emergence of interpersonal trust.…”

“…Our hypotheses (I.B) suggested how such cohesion might affect coordinated social action, social homogeneity, the emergence of group norms at the macro level and, in sufficiently compact groups (I.C), the emergence of interpersonal trust. Watts (1999aWatts ( , 1999b has alerted sociologists to reconsider the problem of "distributed social phenomena" in terms of his models and parameters of "small worlds"-large networks with local clustering of ties but relatively low average distance between members. Connectivity plus conditional density is another model of distributed social phenomena that defines a measure of cohesion not in terms of local clustering but of node-independent paths and invulnerability to disconnection by node removal.…”

“…is less than, equal to, or greater than expected in a "random" distribution. Approximation methods have not yet been developed to answer these questions within random graph theory, although a simulation approach might be useful to bring the emergence of small world cohesivity into the kind of simulation framework developed by Watts (1999a). an edge; their aggregate cohesion measures are given in the fourth row of Table 1: For each successive graph under edge addition, there is an increase in aggregate cohesion.…”

Why Information Should Influence Productivity

“…A network topology that theoretically combines these desired properties is the "small world" topology (Watts and Strogatz 1998;Watts 1999). The small world is defined by two measures: characteristic path length (the smallest number of links it takes to connect one node to another averaged over all pairs of nodes in the network) and the clustering coefficient (the fraction of neighboring nodes that are also collected to one another).…”