# NetMax - Influence Maximization in Social Networks
[](https://pepy.tech/project/netmax)
NetMax is a Python library that provides the implementation of several algorithms for the problem of **Influence Maximization in Social Networks**, originally formulated in "Maximizing the Spread of Influence through a Social Network" (Kempe, Kleinberg and Tardos, 2003). NetMax is built upon NetworkX, a popular python library for working with graphs. It also addresses the problem of Competitive Influence Maximization, as an extensive-form strategic game setting in which multiple entities try to maximize their own influence across the network while minimizing the others'. It works with both signed and unsigned networks, implementing progressive, semi-progressive and non-progressive diffusion models.
Table of Contents:
- [NetMax - Influence Maximization in Social Networks](#netmax---influence-maximization-in-social-networks)
- [Requirements](#requirements)
- [Overview](#overview)
- [Algorithms](#algorithms)
- [Simulation-based](#simulation-based)
- [Proxy-based](#proxy-based)
- [Sketch-based](#sketch-based)
- [Diffusion models](#diffusion-models)
- [Influence probabilities](#influence-probabilities)
- [Endorsement policies](#endorsement-policies)
- [Useful papers](#useful-papers)
- [Example](#example)
- [Credits](#credits)
## Installation
To install the library you can run the following command:
`pip install netmax`
## Requirements
NetMax was developed with Python 3.12 and requires the installation of the following libraries:
- **networkx** (version 3.3)
- **numpy**
- **scipy**
- **tqdm**
- **heapdict**
If you have already installed the library using pip, you don't need to install the requirements, otherwise you can simply run the following command:
`pip install -r requirements.txt`
## Overview
This framework wants to be a useful tool for all those people who study the problem of Influence Maximization. The users instantiate the `InfluenceMaximization` class, setting some basic parameters:
- `input_graph`: a directed graph representing the network (of type `networkx.DiGraph`)
- `agents`: a dictionary where the key is the agent name (`str`) and the value is his budget (`int`)
- `alg`: the algorithm to use for influence maximization (see [Algorithms](#algorithms))
- `diff_model`: the diffusion model to use (see [Diffusion models](#diffusion-models))
- `inf_prob`: the probability distribution used to generate (if needed) the probabilities of influence between nodes. The framework implements different influence probabilities, default is `None` (see [Influence probabilities](#influence-probabilities))
- `endorsement_policy`: the policy that nodes use to choose which agent to endorse when they have been contacted by more than one agent. The framework implements different endorsement policies, default is `'random'` (see [Endorsement policies](#endorsement-policies))
- `insert_opinion`: `True` if the nodes do not contain any information about their opinion on the agents, `False` otherwise (or if the opinion is not used)
- `inv_edges`: a `bool` indicating whether to invert the edges of the graph
- `first_random_seed`: a `bool` indicating whether to insert a first node (chosen randomly) in the seed set of every agent
- `r`: number of simulations to execute (default is 100)
- `verbose`: if `True` sets the logging level to `INFO`, otherwise displays only the minimal information
**Important**: `alg`, `diff_model`, `inf_prob` and `endorsement_policy` can be either `str` or class parameters:
- If they are `str` parameters, they represent the `name` attribute of the corresponding class already present in the framework. This was done in order to prevent the user from directly importing and instantiating all the specific classes, which could have not been user-friendly. To view all the keywords for these parameters, see the corresponding section
- Otherwise, they must extend the corresponding superclass depending on the parameters (`Algorithm` for `alg`, `DiffusionModel` for `diff_model`, `InfluenceProbability` for `inf_prob`, `EndorsementPolicy` for `endorsement_policy`). This way, the user can define his own custom classes
After creating the `InfluenceMaximization` object, the user may call its `run()` method, which returns:
- `seed`: a dictionary where the key is the agent name and the value is the seed set found
- `spread`: a dictionary where the key is the agent name and the value is the expected spread
- `execution_time`: the total execution time (in seconds)
All these values are also available in the `result` attribute (which is a dictionary) of the `InfluenceMaximization` object.
### Algorithms
NetMax provides the implementation of many state-of-the-art algorithms.
#### Simulation-based
- **Monte-Carlo Greedy**: implemented by the class `MCGreedy` (**keyword**: `mcgreedy`)
- **CELF**: implemented by the class `CELF` (**keyword**: `celf`)
- **CELF++**: implemented by the class `CELF_PP` (**keyword**: `celfpp`)
#### Proxy-based
- **Highest Out-Degree Heuristic**: implemented by the class `HighestOutDegree` (**keyword**: `outdeg`)
- **Degree Discount**: implemented by the class `DegDis` (**keyword**: `degdis`)
- **Group PageRank**: implemented by the class `Group_PR` (**keyword**: `group_pr`)
#### Sketch-based
- **StaticGreedy**: implemented by the class `StaticGreedy` (**keyword**: `static_greedy`)
- **RIS**: implemented by the class `RIS` (**keyword**: `ris`)
- **TIM**: implemented by the class `TIM` (**keyword**: `tim`)
- **TIM+**: implemented by the class `TIMp` (**keyword**: `tim_p`)
### Diffusion models
The supported diffusion models are:
- **Independent Cascade**: implemented by the class `IndependentCascade` (**keyword**: `ic`)
- **Linear Threshold**: implemented by the class `LinearThreshold` (**keyword**: `lt`)
- **Triggering Model**: implemented by the class `Triggering` (**keyword**: `tr`)
- **Decreasing Cascade**: implemented by the class `DecreasingCascade` (**keyword**: `dc`)
- **Semi-Progressive Friend-Foe Dynamic Linear Threshold**: implemented by the class `SemiProgressiveFriendFoeDynamicLinearThreshold` (**keyword**: `sp_f2dlt`)
- **Non-Progressive Friend-Foe Dynamic Linear Threshold**: implemented by the class `NonProgressiveFriendFoeDynamicLinearThreshold` (**keyword**: `np_f2dlt`)
### Influence probabilities
The influence probabilities are used to label the edges between the network nodes if they are not already labeled. The user can choose between:
- A **constant** value, set by default at `0.1` (**keyword**: `constant`)
- A **uniform** distribution between `0.01` and `0.1` (**keyword**: `uniform`)
- A distribution based on **similarity** between nodes computed with SimRank algorithm (**keyword**: `similarity`)
- A **ratio model** which distributes the probability uniformly based on the in-degree of the target node (**keyword**: `ratio`)
- A **hybrid** approach based on the average degree of the graph (**keyword**: `hybrid`)
- An **opinion-based** approach (**keyword**: `opinion`) which assigns to each node a vector of **opinions** (namely, values between `0` and `1`) and computes the influence probability comparing the opinions of the two nodes
with cosine similarity and taking into account also their SimRank similarity, with the formula:
$p(u,v)=b+k*\left(\frac{1}{outdeg(u)}*similarity(u,v)+cossim(opinion(u),opinion(v))\right)$
### Endorsement policies
In the competitive setting it is possible that, in the same time step, multiple agents contact the same node. Therefore, it is necessary an endorsement policy that dictates which agent the
node chooses to endorse. Several endorsement policies are implemented:
- A **random** policy, which chooses randomly between the agents that contacted the node in that specific time step (**keyword**: `random`)
- A **voting-based** policy, which chooses the most occurring agent between the already activated neighbors of the node (**keyword**: `voting`)
- A **community-based** approach, which applies the voting strategy to the community the node belongs to instead of its neighbors (**keyword**: `community`)
- A **similarity-based** policy, which essentially is a weighted voting strategy based on the SimRank similarity between the node and its neighbors (**keyword**: `sim_endorsement`)
## Useful papers
Here is a non-exhaustive list of useful papers which have been studied thoroughly to develop this framework:
- Bharathi et al. - Competitive Influence Maximization in Social Networks
- Borgs et al. - Maximizing Social Influence in Nearly Optimal Time
- Borodin et al. - Threshold Models for Competitive Influence in Social Networks
- Budak et al. - Limiting the Spread of Misinformation in Social Networks
- Carnes et al. - Maximizing influence in a competitive social network
- Chen et al. - Efficient Influence Maximization in Social Networks
- Chen et al. - StaticGreedy Solving the Scalability-Accuracy Dilemma in Influence Maximization
- Goyal et al. - CELF++ Optimizing the Greedy Algorithm for Influence Maximization in Social Networks
- Goyal et al. - Learning Influence Probabilities In Social Networks
- Goyal et al. - SimPath An Efficient Algorithm for Influence Maximization under the Linear Threshold Model
- Gursoy et al. - Influence Maximization in Social Networks Under Deterministic Linear Threshold Model
- Huang et al. - Competitive and complementary influence maximization in social network A follower's perspective
- Kempe et al. - Influential Nodes in a Diffusion Model for Social Networks
- Kempe et al. - Maximizing the Spread of Influence through a Social Network
- Kong et al. - Online Influence Maximization under Decreasing Cascade Model
- Leskovec et al. - Cost-Effective Outbreak Detection in Networks
- Li et al. - GetReal Towards Realistic Selection of Influence Maximization Strategies in Competitive Networks
- Lin et al. - A Learning-based Framework to Handle Multi-round Multi-party Influence Maximization on Social Networks
- Liu - Influence maximization in social networks An ising-model-based approach
- Liu et al. - Influence Maximization over Large-Scale Social Networks A Bounded Linear Approach
- Lu et al. - From Competition to Complementarity Comparative Influence Diffusion and Maximization
- Calio, Tagarelli - Complex influence propagation based on trust-aware dynamic linear threshold models
- Tang et al. - Influence Maximization in Near-Linear Time A Martingale Approach
- Tang et al. - Influence Maximization Near Optimal Time Complexity Meets Practical Efficiency
- Wang et al. - Community-based Greedy Algorithm for Mining Top-K Influential Nodes in Mobile Social Networks
- Zhou et al. - UBLF An Upper Bound Based Approach to Discover Influential Nodes in Social Networks
- Zhu et al. - Minimum cost seed set for competitive social influence
## Example
The following is a short example of how to create a simple influence maximization game with two agents. The data is read from a `txt` file with a function defined in the `utils.py` file, but alternatively the user can directly input a `networkx.DiGraph` object with the methods provided by **networkx**.
```
import utils
import influence_maximization as im
g = utils.read_adjacency_matrix("../data/network.txt")
# Dictionary <agent_name: agent_budget>
agents = {
'Agent_0': 10
'Agent_1': 10
}
im_instance = im.InfluenceMaximization(input_graph=g, agents=agents, alg='tim_p',
diff_model='ic', inf_prob='random', r=1000,
insert_opinion=False, endorsement_policy='random', verbose=True)
seed, spread, execution_time = im_instance.run()
print(f"Seed sets found: {seed}")
print(f"Spreads: {spread}")
print(f"Total execution time: {execution_time}")
```
## Credits
The creators of NetMax are Lorenzo Bloise and Carmelo Gugliotta.
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"description": "# NetMax - Influence Maximization in Social Networks\n\n[](https://pepy.tech/project/netmax)\n\nNetMax is a Python library that provides the implementation of several algorithms for the problem of **Influence Maximization in Social Networks**, originally formulated in \"Maximizing the Spread of Influence through a Social Network\" (Kempe, Kleinberg and Tardos, 2003). NetMax is built upon NetworkX, a popular python library for working with graphs. It also addresses the problem of Competitive Influence Maximization, as an extensive-form strategic game setting in which multiple entities try to maximize their own influence across the network while minimizing the others'. It works with both signed and unsigned networks, implementing progressive, semi-progressive and non-progressive diffusion models.\n\nTable of Contents:\n\n- [NetMax - Influence Maximization in Social Networks](#netmax---influence-maximization-in-social-networks)\n - [Requirements](#requirements)\n - [Overview](#overview)\n - [Algorithms](#algorithms)\n - [Simulation-based](#simulation-based)\n - [Proxy-based](#proxy-based)\n - [Sketch-based](#sketch-based)\n - [Diffusion models](#diffusion-models)\n - [Influence probabilities](#influence-probabilities)\n - [Endorsement policies](#endorsement-policies)\n - [Useful papers](#useful-papers)\n - [Example](#example)\n - [Credits](#credits)\n\n## Installation\n\nTo install the library you can run the following command:\n\n`pip install netmax`\n\n## Requirements\n\nNetMax was developed with Python 3.12 and requires the installation of the following libraries:\n\n- **networkx** (version 3.3)\n- **numpy**\n- **scipy**\n- **tqdm**\n- **heapdict**\n\nIf you have already installed the library using pip, you don't need to install the requirements, otherwise you can simply run the following command:\n\n`pip install -r requirements.txt`\n\n## Overview\n\nThis framework wants to be a useful tool for all those people who study the problem of Influence Maximization. The users instantiate the `InfluenceMaximization` class, setting some basic parameters:\n\n- `input_graph`: a directed graph representing the network (of type `networkx.DiGraph`)\n- `agents`: a dictionary where the key is the agent name (`str`) and the value is his budget (`int`)\n- `alg`: the algorithm to use for influence maximization (see [Algorithms](#algorithms))\n- `diff_model`: the diffusion model to use (see [Diffusion models](#diffusion-models))\n- `inf_prob`: the probability distribution used to generate (if needed) the probabilities of influence between nodes. The framework implements different influence probabilities, default is `None` (see [Influence probabilities](#influence-probabilities))\n- `endorsement_policy`: the policy that nodes use to choose which agent to endorse when they have been contacted by more than one agent. The framework implements different endorsement policies, default is `'random'` (see [Endorsement policies](#endorsement-policies))\n- `insert_opinion`: `True` if the nodes do not contain any information about their opinion on the agents, `False` otherwise (or if the opinion is not used)\n- `inv_edges`: a `bool` indicating whether to invert the edges of the graph\n- `first_random_seed`: a `bool` indicating whether to insert a first node (chosen randomly) in the seed set of every agent\n- `r`: number of simulations to execute (default is 100)\n- `verbose`: if `True` sets the logging level to `INFO`, otherwise displays only the minimal information\n\n**Important**: `alg`, `diff_model`, `inf_prob` and `endorsement_policy` can be either `str` or class parameters:\n- If they are `str` parameters, they represent the `name` attribute of the corresponding class already present in the framework. This was done in order to prevent the user from directly importing and instantiating all the specific classes, which could have not been user-friendly. To view all the keywords for these parameters, see the corresponding section\n- Otherwise, they must extend the corresponding superclass depending on the parameters (`Algorithm` for `alg`, `DiffusionModel` for `diff_model`, `InfluenceProbability` for `inf_prob`, `EndorsementPolicy` for `endorsement_policy`). This way, the user can define his own custom classes\n\nAfter creating the `InfluenceMaximization` object, the user may call its `run()` method, which returns:\n\n- `seed`: a dictionary where the key is the agent name and the value is the seed set found\n- `spread`: a dictionary where the key is the agent name and the value is the expected spread\n- `execution_time`: the total execution time (in seconds)\n\nAll these values are also available in the `result` attribute (which is a dictionary) of the `InfluenceMaximization` object.\n\n### Algorithms\n\nNetMax provides the implementation of many state-of-the-art algorithms. \n\n#### Simulation-based\n\n- **Monte-Carlo Greedy**: implemented by the class `MCGreedy` (**keyword**: `mcgreedy`)\n- **CELF**: implemented by the class `CELF` (**keyword**: `celf`)\n- **CELF++**: implemented by the class `CELF_PP` (**keyword**: `celfpp`)\n\n#### Proxy-based\n\n- **Highest Out-Degree Heuristic**: implemented by the class `HighestOutDegree` (**keyword**: `outdeg`)\n- **Degree Discount**: implemented by the class `DegDis` (**keyword**: `degdis`)\n- **Group PageRank**: implemented by the class `Group_PR` (**keyword**: `group_pr`)\n\n#### Sketch-based\n\n- **StaticGreedy**: implemented by the class `StaticGreedy` (**keyword**: `static_greedy`)\n- **RIS**: implemented by the class `RIS` (**keyword**: `ris`)\n- **TIM**: implemented by the class `TIM` (**keyword**: `tim`)\n- **TIM+**: implemented by the class `TIMp` (**keyword**: `tim_p`)\n\n### Diffusion models\n\nThe supported diffusion models are:\n\n- **Independent Cascade**: implemented by the class `IndependentCascade` (**keyword**: `ic`)\n- **Linear Threshold**: implemented by the class `LinearThreshold` (**keyword**: `lt`)\n- **Triggering Model**: implemented by the class `Triggering` (**keyword**: `tr`)\n- **Decreasing Cascade**: implemented by the class `DecreasingCascade` (**keyword**: `dc`)\n- **Semi-Progressive Friend-Foe Dynamic Linear Threshold**: implemented by the class `SemiProgressiveFriendFoeDynamicLinearThreshold` (**keyword**: `sp_f2dlt`)\n- **Non-Progressive Friend-Foe Dynamic Linear Threshold**: implemented by the class `NonProgressiveFriendFoeDynamicLinearThreshold` (**keyword**: `np_f2dlt`)\n\n### Influence probabilities\n\nThe influence probabilities are used to label the edges between the network nodes if they are not already labeled. The user can choose between:\n\n- A **constant** value, set by default at `0.1` (**keyword**: `constant`)\n- A **uniform** distribution between `0.01` and `0.1` (**keyword**: `uniform`)\n- A distribution based on **similarity** between nodes computed with SimRank algorithm (**keyword**: `similarity`)\n- A **ratio model** which distributes the probability uniformly based on the in-degree of the target node (**keyword**: `ratio`)\n- A **hybrid** approach based on the average degree of the graph (**keyword**: `hybrid`)\n- An **opinion-based** approach (**keyword**: `opinion`) which assigns to each node a vector of **opinions** (namely, values between `0` and `1`) and computes the influence probability comparing the opinions of the two nodes\n with cosine similarity and taking into account also their SimRank similarity, with the formula:\n\n$p(u,v)=b+k*\\left(\\frac{1}{outdeg(u)}*similarity(u,v)+cossim(opinion(u),opinion(v))\\right)$\n\n### Endorsement policies\n\nIn the competitive setting it is possible that, in the same time step, multiple agents contact the same node. Therefore, it is necessary an endorsement policy that dictates which agent the\nnode chooses to endorse. Several endorsement policies are implemented:\n\n- A **random** policy, which chooses randomly between the agents that contacted the node in that specific time step (**keyword**: `random`)\n- A **voting-based** policy, which chooses the most occurring agent between the already activated neighbors of the node (**keyword**: `voting`)\n- A **community-based** approach, which applies the voting strategy to the community the node belongs to instead of its neighbors (**keyword**: `community`)\n- A **similarity-based** policy, which essentially is a weighted voting strategy based on the SimRank similarity between the node and its neighbors (**keyword**: `sim_endorsement`)\n\n## Useful papers\n\nHere is a non-exhaustive list of useful papers which have been studied thoroughly to develop this framework:\n\n- Bharathi et al. - Competitive Influence Maximization in Social Networks\n- Borgs et al. - Maximizing Social Influence in Nearly Optimal Time\n- Borodin et al. - Threshold Models for Competitive Influence in Social Networks\n- Budak et al. - Limiting the Spread of Misinformation in Social Networks\n- Carnes et al. - Maximizing influence in a competitive social network\n- Chen et al. - Efficient Influence Maximization in Social Networks\n- Chen et al. - StaticGreedy Solving the Scalability-Accuracy Dilemma in Influence Maximization\n- Goyal et al. - CELF++ Optimizing the Greedy Algorithm for Influence Maximization in Social Networks\n- Goyal et al. - Learning Influence Probabilities In Social Networks\n- Goyal et al. - SimPath An Efficient Algorithm for Influence Maximization under the Linear Threshold Model\n- Gursoy et al. - Influence Maximization in Social Networks Under Deterministic Linear Threshold Model\n- Huang et al. - Competitive and complementary influence maximization in social network A follower's perspective\n- Kempe et al. - Influential Nodes in a Diffusion Model for Social Networks\n- Kempe et al. - Maximizing the Spread of Influence through a Social Network\n- Kong et al. - Online Influence Maximization under Decreasing Cascade Model\n- Leskovec et al. - Cost-Effective Outbreak Detection in Networks\n- Li et al. - GetReal Towards Realistic Selection of Influence Maximization Strategies in Competitive Networks\n- Lin et al. - A Learning-based Framework to Handle Multi-round Multi-party Influence Maximization on Social Networks\n- Liu - Influence maximization in social networks An ising-model-based approach\n- Liu et al. - Influence Maximization over Large-Scale Social Networks A Bounded Linear Approach\n- Lu et al. - From Competition to Complementarity Comparative Influence Diffusion and Maximization\n- Calio, Tagarelli - Complex influence propagation based on trust-aware dynamic linear threshold models\n- Tang et al. - Influence Maximization in Near-Linear Time A Martingale Approach\n- Tang et al. - Influence Maximization Near Optimal Time Complexity Meets Practical Efficiency\n- Wang et al. - Community-based Greedy Algorithm for Mining Top-K Influential Nodes in Mobile Social Networks\n- Zhou et al. - UBLF An Upper Bound Based Approach to Discover Influential Nodes in Social Networks\n- Zhu et al. - Minimum cost seed set for competitive social influence\n\n## Example\n\nThe following is a short example of how to create a simple influence maximization game with two agents. The data is read from a `txt` file with a function defined in the `utils.py` file, but alternatively the user can directly input a `networkx.DiGraph` object with the methods provided by **networkx**.\n\n```\nimport utils\nimport influence_maximization as im\n\ng = utils.read_adjacency_matrix(\"../data/network.txt\")\n# Dictionary <agent_name: agent_budget>\nagents = {\n 'Agent_0': 10\n 'Agent_1': 10\n}\nim_instance = im.InfluenceMaximization(input_graph=g, agents=agents, alg='tim_p', \n diff_model='ic', inf_prob='random', r=1000,\n insert_opinion=False, endorsement_policy='random', verbose=True)\nseed, spread, execution_time = im_instance.run()\nprint(f\"Seed sets found: {seed}\")\nprint(f\"Spreads: {spread}\")\nprint(f\"Total execution time: {execution_time}\")\n```\n\n## Credits\n\nThe creators of NetMax are Lorenzo Bloise and Carmelo Gugliotta.\n",
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