Social Network Analysis with Python
This post gives a brief introduction to network analysis and implementing it with Python
Introduction
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration
Definition of Social Network Analysis (SNA)
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Fundamental Concepts
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Graphs
A network is represented by a graph \(G(V,E)\). A graph \(G=(V,E)\) is ordered pair of sets, where \(V\) is denoted as set of vertices or nodes and \(E\) is set of edges or links. The number of elements in $V$ is known as cardinality of \(V\), \(n = |V|\), and also for the edges, \(m = |E|\). An edge \(e_{ij} = (v_i, v_j)\) is pair of vertices (ordered pair for directed graph). Graph can also represented as matrix which known as adjacency matrix \(A^{n \times n}\), and this matrix has nonzero element \(a_{ij}\) when there is an edge \(e_{ij}\).
In figure above describes the undirected graph which has five vertices or nodes and six edges and corresponds to its matrix form which has size of \(5 \times 5\) matrix. Notice that the undirected graph is represented as symmetric matrix. We now use the term of networks, instead of graph, and so for vertices to nodes, and for edges to links.
A network can be undirected or directed. A directed network is also called a digraph. In directed networks, links are called directed links and the order of the nodes in a link reflects the direction: the link \((i,j)\) goes from the source node \(i\) to the target node \(j\). A network can be unweighted or weighted. In a weighted network, links have associated weights: the weighted link \((i,j, w)\) between nodes \(i\) and nodes \(j\) has weight \(w\). A network can be both directed and weighted, in which case it has directed weighted links.
Here is the code for visualizing sample networks using networkx
The maximum number of links in undirected network with \(N\) nodes can be calculated
\[\begin{eqnarray} \label{eq:Lmax} L_{\text{max}} &=& \binom{N}{2} \\ &=& \frac{N!}{2!(N-2)!} \\ &=& \frac{N(N-1)(N-2)!}{2!(N-2)!} \\ &=& \frac{N(N-1)}{2} \end{eqnarray}\]and for directed network is
\[\begin{equation} \label{eq:Lmax_digraph} L_{\text{max}} = N(N-1) \end{equation}\]However, the actual number of links is typically much smaller than the maximum. Therefore, we want to know how much dense the network we have by the fraction of pairs of nodes that are actually connected. This is we called the density of the network, and we can calculated using the following formula
\[\begin{equation} \label{eq:density} d = \frac{L}{L_{\text{max}}} \end{equation}\]Thus, subtitute \(\ref{eq:Lmax}\) to \(\ref{eq:density}\) gives the density of undirected network given \(N\) nodes.
\[\begin{equation} \label{eq:density_undirected} d = \frac{2L}{N(N-1)} \end{equation}\]Similarly, we can calculate the density for directed network by subtituting \(\ref{eq:Lmax_digraph}\) to \(\ref{eq:density}\) and we get
\[\begin{equation} \label{eq:density_digraph} d = \frac{L}{N(N-1)}. \end{equation}\]Network Types
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Network Properties
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Dyadic and Triadic Relationship
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Homophily and Heterophily
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Network Topologies
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Theoretical Background
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Strength of Weak Ties Theory
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Structural Hole Theory
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Small World Network Theory
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Scale-Free Network Model
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Data Collection and Preparation
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Primary Methods for Collecting SNA Data
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Secondary Sources of SNA Data
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Ethical Considerations in Data Collection
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Preparing Data for Analysis
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Network Analysis Methods and Techniques
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Network Centrality
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Clusters and Equivalence
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Visualizing Networks
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Software and Tools for SNA
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
SNA Case Study
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Challenges and Future Directions in Network Analysis
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Conclusion
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.
Resouces and Further Reading
SNA is a powerful tool. It allows us to explore the underlying structure of an organization or network, identifying the formal and informal relationships that drive the formal processes and outcomes. This insight can enable better communication, facilitate change management, and inspire more efficient collaboration.