1 Social networks theory
Definitions and practice
Marija MitroviÄ Dankulov, MarĂa del Mar Alonso-Almeida, Fariya Sharmeen and Agnieszka Lukasiewicz
Introduction
Humans are social beings. Development and organization of societies and the behaviour of individuals are governed and shaped by social interactions (Wasserman & Faust, 1994). That is why it is not surprising that the structure and evolution of social networks are subject of various scientific disciplines, from sociology, economics and transportation studies to mathematics, computer science and physics. Sociologists introduced the term and the idea of social networks at the end of the 19th century to study the emergence of different social phenomena. Further development of this field during the first half of the twentieth century was led by scientists working in the field of psychology, anthropology and mathematics. During this period, scientists started with systematic recordings and analysis of social interactions in small groups, while mathematicians worked on developing a formalism to quantify the structure of social networks graph theory. The development of Information and Communication Technologies (ICT) at the end of the twentieth century and the availability of large data sets about human behaviour attracted the attention of physicists and computer scientists. These disciplines brought new concepts and powerful quantitative methods which further advanced our knowledge about the structure and dynamics of social networks (Sen & Chakrabarti, 2014).
This chapter provides a brief literature review of works on the topic of social networks in transportation studies, economics and physics. All these disciplines use a concept of social network and define it similarly. The differences between these disciplines are research problems and questions related to social networks, as well as their approaches. In the first part of the chapter, we provide a definition and classification scheme of social networks and describe some quantitative measurements of the network structure. In the second part of the chapter, we summarize the most relevant application of social network theory in transportation studies, economics and physics. We pay particular attention to the results, which indicate the connection between the structure of social networks and mobility patterns and travel behaviour of individuals.
Social networks theory
A social network is a theoretical concept used for the quantitative and qualitative description of social entities and relations between them. The social entities, actors, can be individuals, corporate or collective social units. A tie establishes a linkage between a pair of actors, and it can express a relation between two social entities like talking, kinship, friendship or business relations. In mathematical terms, a social network is a set of nodes (vertices), representing actors, and edges (links), representing social ties. Social ties can represent a direct relation, as in friendship or sexual partnersâ networks, or actors can interact indirectly, through artefacts, for example, a network of bloggers (Sen & Chakrabarti, 2014).
Social network analysis is used for exploring and quantifying patterns of relationships that arise among interacting social bodies, mostly individuals. An explicit assumption of such an approach is that indirect relationships in social groups matter. A particular backbone of social network analysis is that it provides standardized mathematical methods for calculating measures of sociality across levels of social organization, ranging from the population and group levels to the individual level (Freeman, 1984; McCowan et al., 2011). The concept of graphically representing social relationships is not new (Foster, Rapoport, & Orwant, 1963). Nevertheless, recent developments and widespread accessibility of network software have enabled easier visualization and exploration of complex social structures.
Social networks can be roughly divided into three classes based on the type of their ties: single-layer, temporal and multiplex networks (Boccaletti, Latora, Moreno, Chavez, & Hwang, 2006; Holme & Saramäki, 2012; Boccaletti et al., 2014). Single-layer networks are used for representation social systems whose actors interact through only one type of interaction, for example network of coworkers in one company. Depending on whether there are one or two types of actors, these networks can be monopartite or bipartite. Weighted networks are used to represent the systems where interactions can be of different strength. Finally, the interactions can be symmetric (undirected networks), as in the network of co-workers where the relationship is mutual or asymmetric (directed networks), where relationships are not reciprocal, such as studentâmentor social network. Temporal networks are used for the representation of networks where ties and nodes are active at certain points in time (Holme & Saramäki, 2012), for example in mobile phone communication networks where phone call has a limited duration. Multiplex or multilayer networks are composed of a multiplicity of overlapping single-layer networks that capture different types of social connection, for instance actors can use different means of communication (phone calls, short message services, or online media) where each layer of a communication network has its own properties and dynamics. The size of this chapter does not allow us to cover all three types of network representations. A detailed description of methods and tools for the quantitative description of these networks can be found in review articles (Boccaletti et al., 2006; Holme & Saramäki, 2012; Boccaletti et al., 2014). Here we present only several quantitative measures used for the description of the topological structure of single-layer binary undirected networks: degree distribution, clustering coefficient and its dependence on node degree, of assortativity index, the dependence of average first neighbour degree on node degree and shortest path. It was shown that these properties are essential for the description of the topological structure of most real complex networks, including social networks (Orsini et al., 2015).
A quantitative description of social and complex networks requires the right set of tools. Graph theory is a natural framework for the mathematical representation of social and complex networks (Boccaletti et al., 2006). A network or a graph consists of two sets: a set of nodes (vertices) and a set of links (edges) that connects those nodes. Two connected nodes are said to be adjacent or neighbouring. The node degree is the number of its first neighbours.
One of the essential topological features of a network is degree distribution P(q) defined as the probability that randomly chosen node has a degree q. The degree distribution is used for quantifying network heterogeneity at the local level and can be estimated as the fraction of nodes in the network having a degree q. The degree distribution is sufficient for a complete description of the structure of uncorrelated complex networks (Boccaletti et al., 2006; Orsini et al., 2015). However, most of the real, complex networks are correlated in the sense nodes with certain values of degree are more likely to be linked to each other. The degree correlations are characterized by conditional probability P(q|qâ) which equals a probability that there is a link between nodes with degrees q and qâ˛. The direct evaluation of conditional probability from the data is often not possible. Degreeâdegree correlations in a network can be estimated using average-nearest-neighbours degree and its dependence-on-node degree. For uncorrelated networks, the average-nearest-neighbours degree is independent of node degree. Correlated networks can be divided into two classes: assortative networks for which the average degree of nearest neighbours grows with q, and is disassortative where the opposite behaviour is observed.
Clustering, or transitivity, is another topological property of the networks which is particularly important for social networks. The clustering coefficient of a node is the probability that two randomly chosen neighbours of a node are also neighbours. It is estimated as a fraction of existing links out of all possible links between neighbours of a node. By averaging clustering coefficients over all nodes, one obtains the network clustering coefficient. Node and network clustering coefficients take the values between 0 and 1. Networks with a high value of clustering coefficient are considered to be clustered.
The shortest path has been one of the most important properties for characterization of network structure. A path between two nodes is an alternating sequence of nodes and edges, in which no node is visited more than once. The path of the minimal length is known as the shortest path. The shortest path of the largest length in the network is known as network diameter. The average shortest path of a network is defined as the mean of geodesic lengths over all pairs of nodes in the network. Most of the real, complex networks have relatively small average shortest-path length compared to their size, which is why they are often called small-world networks. A recent study (Orsini et al., 2015) has shown that small-world property can be explained using degree distribution, degreeâdegree correlation and dependence of clustering coefficient the on node degree.
Real complex networks are characterized by inhomogeneities on the mesoscopic level, also known as communities. The notion of community and the term itself have been proposed in the social sciences (Wasserman & Faust, 1994). In single-layer networks community is defined as a group of nodes more densely connected than with the rest of the network. The detection and quantitative description of the community structure of complex networks have attracted much attention in the past two decades (Fortunato, 2010). The networks can be characterized by different community structure. The community structure can be simple, with distinct communities. However, typical real-world networks have overlapping communities or communities that are hierarchically embedded. A detailed description of different algorithms and methods for finding different types of communities in static single-layered complex networks can be found in the paper by Fortunato (2010).
Social networks in various disciplines
Social networks in transportation studies
In the field of transportation, seminal empirical research on social networks has been documented. Among them are the studies by Wellman, Carrasco and colleagues (Carrasco, Hogan, Wellman, & Miller, 2008; Carrasco, Miller, & Wellman, 2008; Carrasco & Miller, 2005); Axhausen, Frei and Kowald (Axhausen, 2008; Frei & Axhausen, 2008; Kowald & Axhausen, 2012); and Timmermans, Van den Berg, Arentze, Sharmeen and colleagues (van den Berg, Arentze, & Timmermans, 2008, 2009, 2010, 2011, 2012; Sharmeen, Arentze, & Timmermans, 2013, 2014a, 2014b, 2015a, 2015b, 2016, 2017), based in Toronto, Zurich and Eindhoven, respectively. Most of those studies collected primary survey data, asking respondents to report a section of their social networks. Those studies came together into a comparative analysis of personal social network features in different spatial settings (Kowald et al., 2013) and were also combined in a recent book providing a much-needed overview of the relevant studies (Kowald & Axhausen, 2015).
Among the first attempts to understand social networks in transportation studies, is the connected lives study where name generators were employed to collect social network data (Carrasco & Miller, 2005; Carrasco et al., 2008a, 2008b). They focused on social activity generation, explicitly incorporating social network characteristics of each network member (alter) as well as the characteristics of the overall social structure. For a better understanding of the spatial distribution of social activity, they incorporated activity space anchor points, based in the home, institution and public spaces. Simultaneously, they characterized those places based on recurrence â whether these are regular places or not. The role of ICT on social interaction was also investigated.
On the other hand, Axhausen (2008) argued that social network membership influences a personâs mental map, and therefore, the geogra...