Network Science and Graph Analytics

Epidemic spreading Epidemic spreading, also known as disease spreading or disease transmission, refers to the process by which infectious diseases are transmitted from one individual to another within a population. This concept is a fundamental aspect of epidemiology, which is the study of how diseases spread and impact populations. Understanding epidemic spreading is crucial for public health efforts, as it helps in developing strategies to control and mitigate the spread of diseases. Infectious Agent: Epidemics begin with the presence of an infectious agent, such as a virus, bacterium, or parasite, capable of causing disease in humans or other hosts. Hosts: The individuals or organisms that can become infected by the infectious agent are referred to as hosts. Hosts can vary in their susceptibility to the disease, and some may be more resistant than others. Transmission: The transmission of the infectious agent can occur through various mechanisms, including direct contact, respirator...

Community detection network Community detection in a network, also known as graph community detection, is a fundamental task in network analysis and graph theory. It involves identifying groups or communities of nodes (vertices) within a network (graph) where nodes within a community are more densely connected to each other than to nodes outside of the community. These communities often represent meaningful substructures or functional units within a network. Community detection has applications in various fields, including social network analysis, biology, recommendation systems, and more. Here are some key concepts and methods related to community detection in networks: Modularity: Modularity is a measure commonly used to quantify the quality of a community structure within a network. It measures the difference between the number of edges within communities and what would be expected in a random network. Algorithms: There are various algorithms and methods for community detection, inc...

  Centrality Network Centrality in a network refers to the measure of the importance or significance of a node (or sometimes an edge) within that network. It helps identify which nodes play crucial roles in various network processes such as information flow, influence propagation, or resource allocation. Centrality measures are commonly used in network analysis, including social networks, transportation networks, biological networks, and more. There are several types of centrality measures, including: Degree Centrality: This is the simplest centrality measure and is based on the number of connections a node has. In a social network, it would represent how many friends a person has. Nodes with higher degrees are considered more central.   Closeness Centrality: This measure quantifies how quickly a node can reach all other nodes in the network. It is based on the length of the shortest paths from a node to all other nodes. Nodes with shorter average path lengths are considered m...

Degree Distribution Definition: The degree of a node in a network is the number of connections it has to other nodes. Degree distribution, therefore, describes how these degrees are distributed among all the nodes in the network. Types of Networks: In a social network, the degrees represent the number of friends or connections each person has. In a computer network, degrees represent the number of direct connections each computer or router has. In a citation network, degrees represent the number of citations each scientific paper has. T ypes of Degree Distributions: Power-law Distribution: In many real-world networks, the degree distribution follows a power-law, which means that a few nodes have very high degrees (hubs), while most nodes have relatively low degrees. This is known as a scale-free network. Normal Distribution: In some cases, the degrees follow a normal distribution, with most nodes having similar degrees. Exponential Distribution: In certain situations, the degrees may f...

Small World Networks Small world networks are a type of network that exhibit a combination of both local clustering and short path lengths between nodes. They are often used to model and describe various complex systems, including social networks, the internet, biological networks, and more. The concept of small world networks was popularized by mathematicians Duncan J. Watts and Steven Strogatz in the late 1990s. Local Clustering: In small world networks, nodes tend to be highly connected to their immediate neighbors. This means that if node A is connected to node B, and node B is connected to node C, there's a high probability that node A is also connected to node C. This phenomenon is known as local clustering or the clustering coefficient. Short Path Lengths: Despite the local clustering, small world networks also exhibit relatively short average path lengths between nodes. This means that most nodes in the network can be reached from any other node in a small number of step...

Scale Free Network A scale-free network is a type of complex network that exhibits a specific degree distribution pattern. In a scale-free network, the distribution of node degrees (the number of connections or links each node has) follows a power-law distribution, which means that there are a few nodes with a very high degree of connectivity (hubs), while most nodes have relatively few connections. Hubs: Scale-free networks have a small number of highly connected nodes, called hubs, which have a much higher degree than the average node in the network. These hubs play a critical role in the network's structure and resilience. Power-law degree distribution: The degree distribution of nodes in a scale-free network follows a power-law distribution, which means that the probability of a node having a certain degree is inversely proportional to that degree raised to a power. Mathematically, it can be represented as P(k) ~ k^(-γ), where P(k) is the probability of a node having degree k,...