The study of networks evolution has rapidly become a fundamental topic in the social network analysis (SNA) framework (see for instance, Doreian and Stokman, 1997). In very general terms, networks time evolution may be analyzed in two ways: by considering the dynamics of the behavior of the actors/nodes involved within the network or by taking into account the evolution of the network itself over time . The first approach is related to the actor-oriented class of models, in which the actors activate underlying theoretical micro-mechanisms that induce the evolution of social network structures on the macro-level (Snijders 1999, Snijders et al. 2009). The second approach considers network as a system that evolves over time following specific attachment rules (Watts and Strogatz, 1998; Albert and Barabasi, 1999). In this paper we adopt an intermediate approach. From one hand, as in actor-oriented perspective, network observations are viewed as discrete states of the evolution process and the changes in the structure are operated actor-wise. On the other hand we assume that the actor’s choices are guided by a mechanism based on their “global” relational position in the net. We suppose that actors’ choices are governed by the evaluation of their relational distances from the others. We use as relational distance among actors the so-called Euclidean Commute-Time Distance (ECTD) (Jagers, Gobel, 1976; Fouss et al.., 2007), based on the use of some spectral graph theory quantities, as the laplacian matrix of a graph and its pseudo-inverse (Chung, 1997; Bollobas, 2001). This distance has a nice re-interpretation, in SNA terms, because includes, in only one measure, several actor positional characteristics. In our approach, ECTD is used to define a baseline mechanism that explain ties formations when actors do not have any information on the alters except global network information. The proposed approach starts from an observed network on N nodes at time t=0, G(0)(V,E(0)) (with adjacency matrix A(0)) and, at least another state of the same network detected in a different time G(t)(V,E(t)) (with adjacency matrix A(t)). In order to specify the following configurations of the network along the successive discrete time occasions (i.e. time t=1,2,…,K), we focus on actor possible choices in terms of activation of new links but also on the deactivation of old links. In particular, we select two classes of candidate nodes that, at the time t, have to decide their changes: a class of unconnected nodes and a class of connected nodes. By the evaluation of the actors’ ECTD distances in this two classes, we select the candidate actor that will determine the next step in the network evolution process. This approach may be useful to furnish a sort of baseline model for more complex network evolution specifications. In particular, if this mechanism of attachment works, it means that actors do not have access to exogenous information on the alters in the network (i.e. actors of a web social network, firms in an open market).
A relational distance based approach to network evolution
De Stefano Domenico
2009-01-01
Abstract
The study of networks evolution has rapidly become a fundamental topic in the social network analysis (SNA) framework (see for instance, Doreian and Stokman, 1997). In very general terms, networks time evolution may be analyzed in two ways: by considering the dynamics of the behavior of the actors/nodes involved within the network or by taking into account the evolution of the network itself over time . The first approach is related to the actor-oriented class of models, in which the actors activate underlying theoretical micro-mechanisms that induce the evolution of social network structures on the macro-level (Snijders 1999, Snijders et al. 2009). The second approach considers network as a system that evolves over time following specific attachment rules (Watts and Strogatz, 1998; Albert and Barabasi, 1999). In this paper we adopt an intermediate approach. From one hand, as in actor-oriented perspective, network observations are viewed as discrete states of the evolution process and the changes in the structure are operated actor-wise. On the other hand we assume that the actor’s choices are guided by a mechanism based on their “global” relational position in the net. We suppose that actors’ choices are governed by the evaluation of their relational distances from the others. We use as relational distance among actors the so-called Euclidean Commute-Time Distance (ECTD) (Jagers, Gobel, 1976; Fouss et al.., 2007), based on the use of some spectral graph theory quantities, as the laplacian matrix of a graph and its pseudo-inverse (Chung, 1997; Bollobas, 2001). This distance has a nice re-interpretation, in SNA terms, because includes, in only one measure, several actor positional characteristics. In our approach, ECTD is used to define a baseline mechanism that explain ties formations when actors do not have any information on the alters except global network information. The proposed approach starts from an observed network on N nodes at time t=0, G(0)(V,E(0)) (with adjacency matrix A(0)) and, at least another state of the same network detected in a different time G(t)(V,E(t)) (with adjacency matrix A(t)). In order to specify the following configurations of the network along the successive discrete time occasions (i.e. time t=1,2,…,K), we focus on actor possible choices in terms of activation of new links but also on the deactivation of old links. In particular, we select two classes of candidate nodes that, at the time t, have to decide their changes: a class of unconnected nodes and a class of connected nodes. By the evaluation of the actors’ ECTD distances in this two classes, we select the candidate actor that will determine the next step in the network evolution process. This approach may be useful to furnish a sort of baseline model for more complex network evolution specifications. In particular, if this mechanism of attachment works, it means that actors do not have access to exogenous information on the alters in the network (i.e. actors of a web social network, firms in an open market).Pubblicazioni consigliate
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