Python图与网络分析实战

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"Python for Graph and Network Analysis" 是一本由 Mohammed Zuhair Al-Taie 和 Seifedine Kadry 合著的书籍，探讨了如何使用 Python 进行图和网络分析。这本书属于 Springer 出版社的 Advanced Information and Knowledge Processing 系列，拥有国际标准书号（ISBN）和 DOI，旨在帮助读者理解和应用 Python 在大数据和网络分析领域的技术。在当今这个互联网快速发展的时代，Web 使用模式发生了显著变化。计算机和通信技术的进步激发了人们的创新思维。社交网站如 Twitter、Facebook、LinkedIn 和 Myspace 等大量涌现，促进了新型协作和沟通方式。这些平台使人们能够建立虚拟社交网络，产生了海量的数据，为网络分析提供了丰富的素材。 Python 作为一门强大的编程语言，因其简洁的语法和丰富的库支持，成为进行图论和网络分析的理想工具。本书可能涵盖了以下核心知识点： 1. **图论基础**：介绍图的基本概念，包括节点（vertices）、边（edges）、邻接矩阵、路径和图的度量，如度中心性、接近中心性和介数中心性等。 2. **数据结构**：讲解如何使用 Python 的数据结构（如列表、字典）来表示和操作图，以及专门用于图处理的库，如 NetworkX。 3. **图的生成**：讨论如何生成各种类型的图，包括随机图、有向图、无向图、加权图以及复杂网络模型（如小世界网络和无标度网络）。 4. **网络分析**：涵盖社区检测、聚类系数计算、中心性分析等，帮助理解网络的结构特征和模式。 5. **算法应用**：介绍最短路径算法（如 Dijkstra 和 Bellman-Ford）、遍历算法（如深度优先搜索和广度优先搜索）以及网络优化问题的解决方法。 6. **大数据处理**：结合 Python 的大数据处理库（如 Pandas 和 NumPy），讲解如何处理大规模网络数据。 7. **可视化**：利用 Matplotlib、Seaborn 或者 NetworkX 提供的可视化功能，展示网络的拓扑结构。 8. **案例研究**：书中可能会包含实际案例，比如社交媒体网络分析、交通网络优化或生物网络研究，以帮助读者将理论知识应用于实际场景。通过阅读本书，读者可以掌握 Python 在网络分析中的应用，提升对大数据中复杂关系的理解，以及利用 Python 工具进行网络数据的处理和解析能力。对于科研人员、数据科学家以及对网络分析感兴趣的 IT 专业人士来说，这是一本宝贵的参考资料。

curving back to their nodes. In this case, the value of the main diagonal for any of

these nodes is no more zero.

In addition to the simple representation of relationships between actors using

zeros and ones to indicate the presence or absence of a tie between two nodes as

done in the above table, we can also show the strength of the ties. For example, if

the ties are multiplex, the values in the cells could be the number of different types

of relationships between nodes. Simple metrics like “weak,” “medium,” or “strong”

can also be used to indicate the strength of a relationship between pairs of nodes.

They are translated as one, two, three, respectively. Nodes which have no tie between

them are still coded zero (Table1.2).

1.2.4 Homophily

An important requirement for the study of social networks is the identication of

groups and the study of the relations between them. It is an important driver for

maintaining stability in human and animal social communities over time, and it is a

major criterion that governs the making of ties in social networks.

Homophily is the tendency of individuals to connect with others who share the

same attitudes and beliefs. The tendency of individuals to associate with similar

others based on gender, education, race, or other socioeconomic characteristics is

very common in social communities. Coordination and cooperation are typically

more successful between people who show some similarity to each other such that

individuals in homophilic relationships are likely to hear about new ideas or ask for

help from each other.

Homophily in the context of online social networking can be understood from

the similarity of users who are using the network in terms of age, educational back-

ground, region, or profession. In the sense of corporate networks, homophily is

translated as the similarity of professional or academic qualications.

Table 1.2 Matrix representation of the sociogram showing strengths of ties

A B C D E

A 0 3 2 0 0

B 0 0 0 0 0

C 0 0 0 1 1

D 0 0 1 0 2

E 0 0 1 2 0

1 Theoretical Concepts ofNetwork Analysis

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1.2.5 Dyads andMutuality

A dyad is a pair of actors in a network potentially connected by a social relation. It

is the simplest possible social group in which the transfer of information between

the two nodes can be fast and easy. Dyads are among the concepts that characterize

social networks. In the realm of corporations, dyadic links between organizations

may allow the exchange of information and knowledge, joint venture, tangible and

intangible resources, board interlocks, and many others. Each dyad can be in one of

the three cases: a positive relationship, a negative relationship, and no relationship

between the nodes of the dyad (empty dyad) (Fig.1.3).

In Fig.1.3a, b, nodes indicate individuals and each edge indicates either a posi-

tive or negative relationship. Figure c shows that node A and node B are not con-

nected by any edge.

1.2.6 Balance andTriads

A triad is a network structure consisting of three actors and three dyads. Given a

complete graph of three actors (triad), we can identify four different types of rela-

tionships, depending on the number of negative relationships between nodes: (a) a

friend of my friend is my friend, (b) an enemy of my enemy is my friend, (c) a friend

of my friend is my enemy, and (d) an enemy of my enemy is my enemy.

Once a sign is given to a link, the next question would be: how does that sign is

going to interact with other signs in its local vicinity or with other signs at the net-

work level?

Structural balance theory is the key concept in many applications of the signed

graph theory. It tries to explain how a specic pattern of negative and positive signs

can result in a different kind of relationships. The theory considers the possible

ways in which triads can be signed: triads with an odd number of “+” edges are bal-

anced, while triads with an even number of “-” edges are unbalanced. Imbalanced

graph congurations usually create stress for individuals located on them.

Both the structural balance theory and signed graphs were developed to solve the

subgrouping problem in social psychology. However, they found applications in

other elds as well. They were found very helpful in predicting and explaining

friendships and animosity changes in human communities, which is useful in the

Fig. 1.3 Types of the relationships between two nodes

1.2 Network Measurements

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analysis of enmity in tribal wars, political conicts, or international relations. Let’s

consider a graph with four states as follows (Fig.1.4).

The above graph is a type of signed graphs which have been studied since the

1950s. They are a special case of valued graphs in which ties are allowed to have

one of two opposing values to convey the positive or negative sentiment. Examples

of signed graphs include friend/foe, trust/distrust or like/dislike, esteem/disesteem,

praise/blame, inuence/negative inuence, etc. They are very common in sociology

and psychology but less common in elds such as physics and chemistry.

• In gure a, all the three actors have positive feelings, and there is no place for

conict among them. The conguration is coherent and lacks inner tensions

between members.

• Figure b is also stable since two actors (B and C) share the same negative feeling

towards actor A, but they like each other.

• Figure c is unstable because actors A and B have a negative feeling towards each

other, while both have a positive feeling towards actor C which has to divide its

loyalty between the other two actors.

• Figure d is also unstable and will eventually break down, as it has an odd number

of negative signs.

In Fig.1.4a, b, types of balanced subgraphs are shown, whereas in Fig.1.4c, d,

types of unbalanced graphs are presented. An obvious way to avoid unbalances in

subgraphs is by sign shifting, which includes changing signs such that enmities

(negative signs) become friendships (positive signs) or vice versa. Within real net-

works, stable congurations appear far more often than unstable congurations.

It should be noted here that a negative sign between two nodes does not mean the

lack of tie between these two nodes. While a negative sign between two nodes is a

clear mark of an inimical relationship, the absence of a tie between these nodes sug-

gests the absence of interaction or communication between them.

Fig. 1.4 Graph with three nodes in four states

1 Theoretical Concepts ofNetwork Analysis

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1.2.7 Reciprocity

Reciprocity is a measure of the tendency towards building mutually directed con-

nections between two actors. It refers to the number of reciprocated tie for a specic

actor in a network. For example, if u connects to v, then v connects to u and vice

versa. In real life scenarios, it is important to know whether received help is also

given or whether given help is translated as help by the receiver.

For a given node v, reciprocity is the ratio between the number of nodes which

have both incoming and outgoing connections from/to v, to the number of nodes

which only have incoming connections from v. For an entire network, reciprocity is

calculated as the fraction of edges that are reciprocated. Average reciprocity is cal-

culated by averaging reciprocity values of all nodes in the network.

Reciprocity can be an indicator of the importance of a relationship between two

actors. While a one-way relationship allows the transfer of information (e.g., mes-

sages) from only one side to another, a mutual relationship by this denition is

stronger as it permits the transfer in both directions. In some cases, the relationship

is skewed (i.e., information transfer in one direction is bigger than the other direc-

tion) toward one of the two actors, which can be an indication of differences in

status and power between the two sides.

In friendship networks, such as Facebook.com, and since all friendship connec-

tions are expected to be mutual, reciprocity is 1 (or 100% if by percentage). However,

this is not true for other online social networks (such as Twitter.com) where the

“follow” model is the one that is used to represent relations.

1.3 Network Distribution

Measurements of network distribution are related to how nodes and edges are dis-

tributed in a network.

1.3.1 Distance Between Two Nodes

Distance is a network metric that allows the calculation of the number of edges

between any pair of nodes in a network. Measuring distances between nodes in

graphs is critical for many implementations like graph clustering and outlier detec-

tion. Sometimes, the distance measure is used to see if the two nodes are similar or

not. Any commonly used shortest path calculation algorithm (e.g., Dijkstra) can be

used to provide all shortest paths in a network with their lengths.

We can use the distance measure to calculate node eccentricity, which is the

maximum distances from a given node to all other nodes in a network. It is also

1.3 Network Distribution

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possible to calculate network diameter, which is the highest eccentricity of its nodes

and thus represents the maximum distance between nodes.

In most social networks, the shortest path is computed based on the cost of tran-

sition from one node to another such that the longer the path value, the greater the

cost.

Within a community, there might be many edges between nodes, but between

communities, there are fewer edges.

1.3.2 Degree Centrality

In degree centrality metric, the importance of a node is determined by how many

nodes it is connected to. It is a measurement of the number of direct links to other

actors in the network. This means that the larger the number of adjacent nodes, the

more important the node since it is independent of other actors that reach great parts

of the network. It is a local measure since its value is computed based on the number

of links an actor has to the other actors directly adjacent to it. Actors in social net-

works with a high degree of centrality serve as hubs and as major channels of

information.

In social networks, for example, node degree distribution follows a power law

distribution, which means that very few nodes have an extremely large number of

connections. Naturally, those high-degree nodes have more impact in the network

than other nodes and thus are considered more important. A node i’s degree central-

ity d(i)can be formulated as

where m

=1 if there is a link between nodes i and j and m

=0 if there is no such

link. For directed networks, it is important to differentiate between the in-degree

centrality and the out-degree centrality.

Identifying individuals with the highest-degree centrality is essential in network

analysis because having many ties means having multiple ways to fulll the require-

ments of satisfying needs, becoming less dependent on other individuals, and hav-

ing better access to network resources. Persons with the highest-degree centrality

are often third parties and deal makers and able to benet from this brokerage. For

directed networks, in-degree is often used as a proxy for popularity (Fig.1.5).

The above gure shows that node A and node B are at exceptional structural

positions. All communications lines must go through them. This gives us a conclu-

sion that both nodes, A and B, are powerful merely because of their excellent posi-

tions. However, such a nding is largely based on the nature of links and the nature

of embedded relationships.

1 Theoretical Concepts ofNetwork Analysis

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