Metrics of Evolving Ego-Networks with Forgetting Factor

Metrics of Evolving Ego-Networks with Forgetting Factor

Rui Portocarrero Sarmento (University of Porto, Faculty of Engineering, Porto, Portugal)
DOI: 10.4018/IJSODIT.2017010103
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Abstract

Nowadays, treating the data as a continuous real-time flux is an exigence explained by the need for immediate response to events in daily life. We study the data like an ongoing data stream and represent it by streaming egocentric networks (Ego-Networks) of the particular nodes under study. We use a non-standard node forgetting factor in the representation of the network data stream, as previously introduced in the related literature. This way the representation is sensible to recent events in users' networks and less sensible for the past node events. We study this method with large scale Ego-Networks taken from telecommunications social networks with power law distribution. We aim to compare and analysis some reference Ego-Networks metrics, and their variation with or without forgetting factor.
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Several studies were presented regarding ego-networks in the scope of social network analysis. The areas are varied between biology, sociology to criminal networks. In this section, the authors introduce related work in a wider scope by mentioning publications regarding social networks, which include information about ego-networks.

Ego-Networks

In (Hanneman & Riddle, 2005), a throughout exposition about social networks is made, and a full chapter is dedicated to ego-networks. Hanneman et al. define “ego” as an individual “focal” node in a network. “neighborhood” sets the boundaries of ego networks and includes all the direct connections and egos that tie with an ego. Dejordy et al. (Dejordy & Halgin, 2009), introduce the network perspective and the differences between socio-centric and ego-centric analysis. The ego-centric approach fits studies about phenomena or entities across different networks. The socio-centric approach is more suitable for studying interaction within a defined network.

Wasserman et al. provide a complete study of social networks with several models in (Wasserman & Faust, 1994). Some relevant studies address the social structure of competition.

For Burt et al. (Burt, 1992), the social structure of competition addresses the consequences of voids in relational and resource networks. Competitive behavior can be understood regarding player access to “holes” in the social structure of the competitive arena. Those “structural holes” create entrepreneurial opportunities for information access, timing, referrals, and control. Ego-networks analysis provides an answer to this sensible information or properties that are also studied in the Case Study section of this document.

Figure 1 represents two ego-networks with connections to the 4th and 2nd order, respectively for node 1 and 5. This example shows how the same network change in terms of visualization, depending on the selected ego node.

Figure 1.

Ego-Network visualization: (a) selected ego node 1 and (b) Ego-Network centered in node 1; (c) same network but with ego node 5 and (d) Ego-Network centered in node 5.

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