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L. L. Benites-Lazaro et al.
as well as more advanced structural statistics, such as the centrality of the vertices in
the network and the prestige indexes (Centrality of proximity, Centrality of Interest,
Prestige Proximity, etc.), and groupings and triads (grouping coefficient, triad census)
[9]. Historically, SNA was one of the first analytical tools in using graph theory [41].
It emerged due to the need to make the social sciences somewhat more formal,
which gave rise to sociometry. One of its strands used statistics to study populations
(macro-level), another used graph theory to model relationships between people
(micro-level), following the idea of the genealogical trees of anthropology [9, 41].
There are at least four ways to approaching the study of social networks, either by
the general characteristics that it presents, by the position of the actors, by the groups
that conform it, or by the visualization of them. First, it is possible to identify that there
are many types of networks that have not yet been classified, but there are already very
frequent phenomena in them. An example of such social networks is the so-called
six degrees of separation [25]. This phenomenon is also known as small world [33]
and occurs in networks with special connectivity whereby the half distance between
two actors is very small in comparison to the size (number of actors) of the network.
In other networks, such as quotes from scientific articles, and the internet among,
the distribution of degrees follows a power law or similar. These networks are called
scale-free networks because in a subgraph of this type of network, the degrees are
still likely to be distributed as power law. Scale-free networks are interesting because
they repeat in many other cases, such as in the distribution of tickets (Effect Matheus)
[32]. Phenomena with these properties continue to be observed time and again.
Second, the concept of the locational position of an actor in a network corresponds to the access it has to the rest of the network. In principle two actors are
known to occupy the same place in a given network if they share the same neighbors (i.e., structural equivalence, which is a local version of edge isomorphism).
Measures of centrality have typically been used as proxies for influence and power,
and have enabled research to be carried out on brokerage relationship [41]. A person
located in the center of a star is assumed to be structurally more central than any other
person in any other position in any other similar sized network [20]. There are four
measures of centrality that are widely used in network analysis: degree centrality,
betweenness, closeness, and eigenvector centrality. Centrality measures attempt to
quantify how central each person or topic is inside a given social network. To that
end, these measures usually examine both the ties attached to an actor as well as the
geodesic distances (shortest path lengths) to other actors [22].
Third, the detection of communities, groups, ghettos (exclusive groups), etc. that
form the network, are of great interest in the study of social networks. It is complicated
because it is not easy to define a group. The definition becomes easy when there is a
formal structure involved, or when there is a defined group and “a group” of adherents
that are said to be part of the group (e.g., Brazil and Brazilians). However, this
becomes complex, obscure, and even esoteric when it comes to informal structures.
A group of friends represent a lot of people, in which all or most are friends with
one another, but members of this group also have friends in common from outside
the group, therefore it can be difficult to defines who belong to the group and who
does not. There are many techniques to detect groups, and many algorithms that obey
L. L. Benites-Lazaro et al.
as well as more advanced structural statistics, such as the centrality of the vertices in
the network and the prestige indexes (Centrality of proximity, Centrality of Interest,
Prestige Proximity, etc.), and groupings and triads (grouping coefficient, triad census)
[9]. Historically, SNA was one of the first analytical tools in using graph theory [41].
It emerged due to the need to make the social sciences somewhat more formal,
which gave rise to sociometry. One of its strands used statistics to study populations
(macro-level), another used graph theory to model relationships between people
(micro-level), following the idea of the genealogical trees of anthropology [9, 41].
There are at least four ways to approaching the study of social networks, either by
the general characteristics that it presents, by the position of the actors, by the groups
that conform it, or by the visualization of them. First, it is possible to identify that there
are many types of networks that have not yet been classified, but there are already very
frequent phenomena in them. An example of such social networks is the so-called
six degrees of separation [25]. This phenomenon is also known as small world [33]
and occurs in networks with special connectivity whereby the half distance between
two actors is very small in comparison to the size (number of actors) of the network.
In other networks, such as quotes from scientific articles, and the internet among,
the distribution of degrees follows a power law or similar. These networks are called
scale-free networks because in a subgraph of this type of network, the degrees are
still likely to be distributed as power law. Scale-free networks are interesting because
they repeat in many other cases, such as in the distribution of tickets (Effect Matheus)
[32]. Phenomena with these properties continue to be observed time and again.
Second, the concept of the locational position of an actor in a network corresponds to the access it has to the rest of the network. In principle two actors are
known to occupy the same place in a given network if they share the same neighbors (i.e., structural equivalence, which is a local version of edge isomorphism).
Measures of centrality have typically been used as proxies for influence and power,
and have enabled research to be carried out on brokerage relationship [41]. A person
located in the center of a star is assumed to be structurally more central than any other
person in any other position in any other similar sized network [20]. There are four
measures of centrality that are widely used in network analysis: degree centrality,
betweenness, closeness, and eigenvector centrality. Centrality measures attempt to
quantify how central each person or topic is inside a given social network. To that
end, these measures usually examine both the ties attached to an actor as well as the
geodesic distances (shortest path lengths) to other actors [22].
Third, the detection of communities, groups, ghettos (exclusive groups), etc. that
form the network, are of great interest in the study of social networks. It is complicated
because it is not easy to define a group. The definition becomes easy when there is a
formal structure involved, or when there is a defined group and “a group” of adherents
that are said to be part of the group (e.g., Brazil and Brazilians). However, this
becomes complex, obscure, and even esoteric when it comes to informal structures.
A group of friends represent a lot of people, in which all or most are friends with
one another, but members of this group also have friends in common from outside
the group, therefore it can be difficult to defines who belong to the group and who
does not. There are many techniques to detect groups, and many algorithms that obey