Table 1 Network models and their characteristics

Jozef Sumec

Regular lattices

Simple models of networks. Suitable for solving analytic problems.

Unrealistic compared with real networks.

Erdos and Renyi [35]

Random regular network

Simple prototype of network, homogeneous.

Too restrictive.

Watts and Strogatz [26]

Small world networks

Realistic roused from social networks.

With a power-law basis, it is unable to construct heterogeneous degree distribution.

Barbasi and Albert [28]

Barbasi Albert model

Appropriate for generating the time growth characteristic among several real—world networks.

Model of emergence graph.

The dynamic process is treated as static in this network.

Fitness of nodes is not considered for making new links.

Bianconi and Barbasi [41]

Fitness model

Similar to BA model.

Consider degree and fitness of nodes for making new connections.

Does not predict the impact of homophily.

Almeida et al. [42]

Homophilic model

Consider similitude of nodes.

Model of emergence of small-world features and power-law degree distribution.

Produces undirected networks, It faces some difficulties in extending this model to directed networks.

Catanzaro et al. [43]

Uncorrelated random networks

It is important for checking theoretical solutions of the interactions of dynamical systems.

Unusual in real networks.

Waxman [36]

Spatial Waxman model

generalization of the Erdos–Renyi graph

Consider geographical properties.

Weak in the prediction of most real systems.

Rozenfeld et al. [11]

Scale free on lattice

When creating new links, keep the Euclidean distance between nodes in consideration.

The entire length of the system's links can be kept to a minimum.

Perra et al. [37]

Activity driven model

Actor action drives relationships.

Example of temporal social network.

Do not consider other features of actor activity like different weights associated with each connection.

Gross et al. [44]

Adaptive networks

Useful to model many real systems.

With adaptive way, topologies change with changes of node’s states.

There is yet no clear theoretical explanation for large-scale adaptive network limitations.

Colizza and Vespignani [39]

Metapopulation model

A network of networks that describes a connected population.

Widely used because of the mobility of node.

In spatial epidemiology, it is difficult to represent the essential aspects of spatial transmission of infectious diseases [45].

Mucha et al. [40]

Multilayer networks

The dynamic process has the potential to propagate inside and between layers.

The spectral characteristics of the graph can be used to identify distinct multiplexity regimes and coupling between layers [46].