import React, { Component } from 'react';
import { View, Text, Button, TextInput } from 'react-native';

class MyComponent extends Component {
constructor(props) {
  super(props);
}

render() {
  return (
    <View >
      <Button title="My Component"/>
    </View>
  )
}
}
export default MyComponent;

import React from 'react';
import { configure, shallow } from 'enzyme';
import Adapter from 'enzyme-adapter-react-16';
import MyComponent from '../components/MyComponent.js';

configure({ adapter: new Adapter() })  //setting up enzyme

const styles = require('../styles.js');

describe('rendering', () => {
  it('checking View and Button exists', () => {
    let wrapper
    wrapper = shallow(<MyComponent/>);

    expect(wrapper.find('View').children().find('Button')).toHaveProperty('title','My Component')
    });
    })
});

Expected the object:
 < listing of full object...>
To have a nested property:
  "title"
With a value of:
  "My Component"