# What is a Social Network?

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A social network is a heterogeneous and multi-relational information set described by a graph. The graph is generally very large, with nodes corresponding to objects and edges corresponding to connections describing relationships or connections between objects. Both nodes and connections have attributes. Objects can have class labels. Links can be one-directional and are not needed to be binary.

A social network is a heterogeneous and multi-relational information set described by a graph. The graph is generally very large, with nodes corresponding to objects and edges corresponding to connections describing relationships or connections between objects. Both nodes and connections have attributes. Objects can have class labels. Links can be one-directional and are not needed to be binary.

## Characteristics of Social Networks

There are the following characteristics of social network which are as follows −

• Densification power-law − It was considered that as a network evolves, the number of degrees increases linearly in the multiple nodes. This was called the constant average degree hypothesis. But, extensive experiments have displayed that, viceversa,networks become denser over time with the average degree increasing (and therefore, the number of edges increasing super linearly in the number of nodes).The densification follows the densification power law (or growth power-law), which defines

$$e(t)\propto n(t)^{a}$$

where e(t) and n(t), respectively, define the number of edges and nodes of the graph at time t, and the exponent a generally lies strictly among 1 and 2. If a = 1, this corresponds to a fixed average degree over time, whereas a = 2 corresponds to a completely dense graph where each node has edges to a fixed fraction of all nodes.

• Shrinking diameter − It has been experimentally shown that the efficient diameter tends to reduce as the network increases. This contradicts an earlier understanding that the diameter slowly increases as a service of network size.

Consider a citation web, where nodes are papers and a citation from one paper to another is denoted by a directed edge. Outlinks of a node, v (defining the papers cited by v), are “frozen” at the moment it combines the graph. The decreasing distances among pairs of nodes consequently occur to be the result of subsequent papers acting as “bridges” by citing earlier papers from several areas.

• Heavy-tailed out-degree and in-degree distributions − The multiple out-degrees for a node tend to follow a heavy-tailed distribution by observing the power law, 1/na , where n is the rank of the node in the order of decreasing out-degrees and generally, 0 < a < 2.

The smaller the value of a the heavier the tail. This phenomenon is defined in the preferential connection model, where each new node connects to an existing network by a fixed number of out-links, following a rich-get-richer rule. The indegrees also follow a heavy-tailed distribution, although its influence is more skewed than the out-degrees distribution.